CourceMeterials-MTECHEC13

MSET3 : MODERN DIGITAL COMMUNICATION TECHNOLOGY

1. ELECTRONIC COMMUNICATION SYSTEM

Introduction, Contaminations, Noise, The Audio Spectrum, Signal Power Units, Volume Unit ,

Signal-To-Noise Ratio, Analog And Digital Signals, Modulation, Fundamental Limitations In A

Communication System, Number Systems

2. SAMPLING AND ANALOG PULSE MODULATION

Introduction, Sampling Theory, Sampling Analysis, Types Of Sampling, Practical Sampling:

Major Problems, Types Of Analog Pulse Modulation, Pulse Amplitude Modulation, Pulse

Duration Modulation, Pulse Position Modulation, Signal-To-Noise Ratios In Pulse Systems

3. DIGITAL MODULATION: DM AND PCM

Introduction, Delta Modulation, Pulse.Code Modulation , PCM Reception And Noise,

Quantization Noise Analysis, Aperture Time, The S N Ratio And Channel Capacity Of PCM,

Comparison Of PCM With Other Systems, Pulse Rate, Advantages Of PCM, Codecs, 24-

Channel PCM, The PCM Channel Bank, Multiplex Hierarchy, Measurements Of Quantization

Noise, Differential PCM

4. DIGITAL DATA TRANSMISSION

Introduction, Representation Of Data Signal, Parallel And Serial Data Transmission, 20ma Loop

And Line Drivers, Modems, Type Of Transient Noise In Digital Transmission, Data Signal:

Signal Shaping And Signaling Speed, Partial Response (Correlative) Techniques, Noise And

Error Analysis, Repeaters, Digital-Modulation Systems, Amplitude-Shift Keying (ASK),

Frequency Shift Keying (FSK), Phase-Shift Keying (PSK), Four-Phase Or Quarternary PSK,

Interface Standards

5. COMMUNICATION OVER BANDLIMITED CHANNELS

Definition And Characterization Of 4 Bandlimited Channel, Optimum Pulse Shape Design For

Digital Signaling Through Bandlimited Awgn Channels, Optimum Demodulation Of Digital

Signals In The Presence Of 151 And Awgn, Equalization Techniques, Further Discussion

Unit 1

Electronic Communication System-1

Structure

1.1 Objective

1.2 Introduction

1.3 Contaminations

1.4 Noise

1.5 The Audio Spectrum

1.6 Signal power Units & volume units

1.7 Summary

1.8 Keywords

1.9 Exercise

1.1 Introduction

The fundamental purpose of an electronic communication system is to transfer from one

place to another. Thus, electronic communication can be summarized as the transmission,

reception, and processing of information between two or more locations using electronic circuits.

The original source information can be in analog form, such as the human voice or music, or

digital form, such as binary coded numbers or alphanumeric codes. Analog signals are time

varying voltages or currents that are continuously changing , such as sine and cosine waves. An

analog signal contains an infinite number of values. Digital signals are voltages or currents that

change in discrete steps or levels. The most common form of digital signal is binary, which has

two levels. All forms of information, however, must be converted to electromagnetic energy

before being propagated through an electronic communication system.

1.2 Objective

At the end of this chapter you will be able to:

• Explain Contaminations

• Know types of Noise

• Describe the Audio Spectrum

• Know the Spectral Density of Thermal Noise

1.3 Contaminations

Contamination problems have become a major factor in determining the

manufacturability, quality, and reliability of electronic assemblies. Understanding the mechanics

and chemistry of contamination has become necessary for improving quality and reliability and

reducing costs of electronic assemblies. Designed as a practical guide, Contamination of

Electronic Assemblies presents a generalized overview of contamination problems and serves as

a problem-solving reference point. It takes a step-by-step approach to identifying contaminants

and their effects on electronic products at each level of manufacture.

The text is divided into four sections: Laminate Manufacturing, Substrate Fabrication, Printed

Wiring Board Assembly, and Conformal Coatings. These sections discuss all aspects of

contamination of electronic assemblies, from the manufacture of glass fibers used in the

laminates to the complete assembly of the finished product. The authors present detection and

control methods that can help you reduce defects during the manufacturing process. With tables,

figures, and fishbone diagrams serving as a quick reference, Contamination of Electronic

Assemblies will help you familiarize yourself with the origination, detection, measurement,

control, and prevention of contamination in electronic assemblies.

Features

• Lists sources of contamination throughout the manufacturing process

• Illustrates quality and reliability issues with photos and tables

• Discusses aspects of contamination from the manufacture of the glass fibers used in the

laminates to the complete assembly of the finished product

• Targets defects encountered during the manufacturing process along with the

contaminants causing those defects

• Discusses how defects can be reduced through detection and control methods

1.4 Noise

Electronic noise is a random fluctuation in an electrical signal, a characteristic of

all electronic circuits. Noise generated by electronic devices varies greatly, as it can be produced

by several different effects. Thermal noise is unavoidable at non-zero temperature, while other

types depend mostly on device type or manufacturing quality and semiconductor defects .

Electrical Noise is any unwanted form of energy tending to interfere with the proper and easy

reception and reproduction of wanted signals.

Basic Noise Mechanisms

Consider n carriers of charge e moving with a velocity v through a

sample of length l. The induced current i at the ends of the sample is

The fluctuation of this current is given by the total differential

where the two terms are added in quadrature since they are statistically uncorrelated.

Two mechanisms contribute to the total noise:

• velocity fluctuations, e.g.

• number fluctuations, e.g.

Thermal noise and shot noise are both “white” noise sources, i.e. power per unit bandwidth is

constant:

=spectral density)

whereas for “1/ f ” noise

(typicallya= 0.5 – 2)

1.4.1. Thermal Noise in Resistors

The fluctuation of this current is given by the total differential


Two mechanisms contribute to the total noise:

e.g. thermal noise

e.g. shot noise excess or '1/ f ' noise


1. Thermal Noise in Resistors



The most common example of noise due to velocity fluctuations is the thermal noise of

resistors.

Spectral noise power density vs. frequency

k = Boltzmann constant

T = absolute temperature

Since

R = DC resistance

the spectral noise voltage density

and the spectral noise current density

The total noise depends on the bandwidth of the system. For example, the total noise voltage at

the output of a voltage amplifier with the frequency dependent gain

Note: Since spectral noise components are non

power.


Spectral noise power density vs. frequency f

the spectral noise voltage density

and the spectral noise current density


the output of a voltage amplifier with the frequency dependent gain Av (f) is

Note: Since spectral noise components are non-correlated, one must integrate ov



correlated, one must integrate over the noise

1.4.2. Shot noise

A common example of noise due to number fluctuations is “shot noise”, which occurs

whenever carriers are injected into a sample volume independently of one another.

Example: current flow in a semiconductor diode (emi

Spectral noise current density:

qe= electronic charge

I = DC current

A more intuitive interpretation of this expression will be givenlater.

=Shot noise does not occur in “ohmic” conductors. Since the

number of available charges is not limited, the fields caused

by local fluctuations in the charge density draw in additional

carriers to equalize the total number.

1.4.3. 1/f Noise

The noise spectrum becomes non

random in time, for example whencarriers are trapped and then released with a time constant

=.With an infinite number of uniformly distributed time constantsthe spectral power d

assumes a pure 1/f distribution.However, with as few as 3 time constants spread over one ortwo

decades, the spectrum is approximately 1/

=For a 1/f spectrum the total noise depends on the ratio of theupper to

rather than the absolutebandwidth.



Example: current flow in a semiconductor diode (emission over a barrier)

A more intuitive interpretation of this expression will be givenlater.

=Shot noise does not occur in “ohmic” conductors. Since the

of available charges is not limited, the fields caused

by local fluctuations in the charge density draw in additional

carriers to equalize the total number.

The noise spectrum becomes non-uniform whenever thefluctuations are not purely


=.With an infinite number of uniformly distributed time constantsthe spectral power d

distribution.However, with as few as 3 time constants spread over one ortwo

decades, the spectrum is approximately 1/f, so this form ofnoise is very common.

spectrum the total noise depends on the ratio of theupper to lower cutoff frequencies,

rather than the absolutebandwidth.



uniform whenever thefluctuations are not purely


=.With an infinite number of uniformly distributed time constantsthe spectral power density

distribution.However, with as few as 3 time constants spread over one ortwo

, so this form ofnoise is very common.

lower cutoff frequencies,

Spectral Density of Thermal Noise

Two approaches can be used to derive the spectral distribution of thermal noise.

1. The thermal velocity distribution of the charge carriers is used to calcul

dependence of the induced current, which is then transformed into the frequency domain.

2. Application of Planck’s theory of black body radiation.

The first approach clearly shows the underlying physics, whereas the second “hides” the

physics by applying a general result of statistical mechanics. However, the first requires some

advanced concepts that go well beyond the standard curriculum, so the “black body” approach

will be used.

In Planck’s theory of black body radiation the energy per mod

and the spectral density of the radiated power

i.e. this is the power that can be extracted in equilibrium. At low frequencies

so at low frequencies the spectral density is independent of frequency and for a total bandwidth

the noise power that can be transferred to an external device

To apply this result to the noise of a resistor, consider a resistor

to a noise voltage Vn .To determine the power transferred to an external device

circuit

Spectral Density of Thermal Noise

Two approaches can be used to derive the spectral distribution of thermal noise.

1. The thermal velocity distribution of the charge carriers is used to calcul


2. Application of Planck’s theory of black body radiation.


by applying a general result of statistical mechanics. However, the first requires some


In Planck’s theory of black body radiation the energy per mode

and the spectral density of the radiated power

i.e. this is the power that can be extracted in equilibrium. At low frequencies hv<<kT

so at low frequencies the spectral density is independent of frequency and for a total bandwidth

the noise power that can be transferred to an external device n P=kTB.

To apply this result to the noise of a resistor, consider a resistor R whose thermal noise gives rise

To determine the power transferred to an external device

1. The thermal velocity distribution of the charge carriers is used to calculate the time



by applying a general result of statistical mechanics. However, the first requires some


hv<<kT

so at low frequencies the spectral density is independent of frequency and for a total bandwidth B

whose thermal noise gives rise

To determine the power transferred to an external device consider the

The power dissipated in the load resistor

The maximum power transfer occurs when the load resistance equals the source

resistanceRT = R, so

Since the power transferred to RL

and the spectral density of the noise power

The power dissipated in the load resistor RL

The maximum power transfer occurs when the load resistance equals the source

RL is kTB

the spectral density of the noise power

1.4.4 Spectral Density of Shot Noise

If an excess electron is injected into a device, it forms a current pulse of duration

thermionic diode t is the transit time from cathode to anode (see IX.2), for example. In a

semiconductor diode t is the recombination time (see IX

to the periods of interest t<<1/ f

transform of a delta pulse yields a “white” spectrum, i.e. the amplitude distribution in frequency

is uniform

Within an infinitesimally narrow frequency band the individual spectral components are pure

sinusoids, so their rms value

If N electrons are emitted at the same average rate, but at different times, they will have the same

spectral distribution, but the coefficients will differ in phase. For example, for two currents

iqwith a relative phase =the total rms current

For a random phase the third term averages to zero

so if N electrons are randomly emitted per unit time, the individual spectral components

simply add in quadrature

Spectral Density of Shot Noise

If an excess electron is injected into a device, it forms a current pulse of duration

is the transit time from cathode to anode (see IX.2), for example. In a

is the recombination time (see IX-2). If these times are short with respect

f , the current pulse can be represented by a d pulse



electrons are emitted at the same average rate, but at different times, they will have the same

spectral distribution, but the coefficients will differ in phase. For example, for two currents

the total rms current

random phase the third term averages to zero

electrons are randomly emitted per unit time, the individual spectral components

If an excess electron is injected into a device, it forms a current pulse of duration t. In a

is the transit time from cathode to anode (see IX.2), for example. In a

2). If these times are short with respect

pulse. The Fourier



electrons are emitted at the same average rate, but at different times, they will have the same

spectral distribution, but the coefficients will differ in phase. For example, for two currents ipand

electrons are randomly emitted per unit time, the individual spectral components

The average current

so the spectral noise density

“Noiseless” Resistances

a) Dynamic Resistance

In many instances a resistance is formed by the slope of a device’s current

characteristic, rather than by a static ensemble of electrons agitated by thermal energy.

Example: forward-biased semiconductor diode

Diode current vs. voltage

The differential resistance

i.e. at a given current the diode presents a resistance, e.g. 26

I = 1 mA and T = 300 K.

In many instances a resistance is formed by the slope of a device’s current


biased semiconductor diode

i.e. at a given current the diode presents a resistance, e.g. 26 =at

In many instances a resistance is formed by the slope of a device’s current-voltage


Note that two diodes can have different charge carrier concentrations, but will still exhibit the

same dynamic resistance at a given current, so the dynamic resistance is not uniquely determined

by the number of carriers, as in a resistor.

There is no thermal noise associated with this “dynamic” resistance, although the current

flow carries shot noise.

Radiation Resistance of an Antenna

Consider a receiving antenna with the normalized power pattern

P n(=,Ф) P pointing at a brightness distribution

bandwidth received by the antenna

wheree A is the effective aperture, i.e. the “capture area” of the antenna. For a given field

strength E, the captured power =

If the brightness distribution is from a black body radiator and we’re measuring in the Rayleigh

Jeans regime,

and the power received by the antenna

=A is the beam solid angle of the antenna (measured in rad2), i.e. the angle through which all the

power would flow if the antenna pattern were uniform over its beam width.

Since A e = A=λ=

(see antenna textbooks), the received p

The received power is independent of the radiation resistance, as would be expected for thermal

noise. However, it is not determined by the temperature of the antenna, but by the temperature of

the sky the antenna pattern is subtending.


given current, so the dynamic resistance is not uniquely determined

by the number of carriers, as in a resistor.


Antenna

Consider a receiving antenna with the normalized power pattern

pointing at a brightness distribution B(=,Ф) in the sky. The power per unit

bandwidth received by the antenna

is the effective aperture, i.e. the “capture area” of the antenna. For a given field

=e W EA .

If the brightness distribution is from a black body radiator and we’re measuring in the Rayleigh

eceived by the antenna

is the beam solid angle of the antenna (measured in rad2), i.e. the angle through which all the

power would flow if the antenna pattern were uniform over its beam width.

(see antenna textbooks), the received power



the sky the antenna pattern is subtending.


given current, so the dynamic resistance is not uniquely determined


Ф) in the sky. The power per unit

is the effective aperture, i.e. the “capture area” of the antenna. For a given field

If the brightness distribution is from a black body radiator and we’re measuring in the Rayleigh-

is the beam solid angle of the antenna (measured in rad2), i.e. the angle through which all the



For example, for a region dominated by the CMB, the measured power corresponds to a resistor

at a temperature of ~3K, although the antenna may be at 300K.

Noise characteristics

Both thermal and shot noise are purely random.

• amplitude distribution is Gaussian

• noise modulates baseline

• baseline fluctuations superimposed on signal

• output signal has gaussian distribution

1.5 The Audio Spectrum

The audio spectrum is the audible frequency range at which humans can hear. The range

spans from 20Hz to 20,000Hz and can be effectively broken down into seven different

frequency bands, with each having a different impact on the total sound.

The seven frequency bands are:

Sub-bass > Bass > Low midrange > Midrange >Upper midrange > Presence and Brilliance

Sub Bass: 20 to 60 Hz

Sub Bass Frequencies

The ‘sub bass’ provides the first usable low frequencies on most recordings. The deep bass

produced in this range is usually felt more than it is heard, providing a sense of power. Many

instruments struggle to enter this frequency range, with the exception of a few bass heavy

instruments, such as the bass guitar which has a lowest achievable pitch of 41 Hz. It is difficult to

hear any sound at low volume level around the 'sub bass' range because of the Fletcher Munson

curves.

It is recommended that no or very little boost is applied to this region without the use of very

high quality monitor speakers.

Too much boost in the sub-bass range can make the sound ‘too powerful’, whereas too much cut

will weaken and thin out the sound.

Bass: 60 to 250 Hz

Bass Frequencies

The ‘bass’ range determines how fat or thin the sound is. The fundamental notes of rhythm are

centred on this area. Most bass signals in modern music tracks lie around the 90-200Hz area. The

frequencies around 250 Hz can add a feeling of warmth to the bass without loss of definition.

Too much boost in the 'bass' region tends to make the music sound boomy.

Low Midrange: 250 to 500 Hz

Low Midrange Frequencies

The 'low midrange' contains the low order harmonics of most instruments and is generally

viewed as the bass presence range. Boosting a signal around 300 kHz adds clarity to the bass

and lower-stringed instruments. Too much boost around 500 kHz can make higher-frequency

instruments sound muffled.

Beware that many songs can sound muddy due to excess energy in this region.

Midrange: 500 to 2 kHz

Midrange Frequencies

The 'midrange' determines how prominent an instrument is in the mix. Boosting around 1000

kHz can give instruments a horn like quality. Excess output at this range can sound tinny and

may cause ear fatigue. If boosting in this area, be very cautious, especially on vocals. The ear is

particularly sensitive to how the human voice sounds and its frequency coverage.

Upper Midrange: 2 kHz to 4 kHz

Upper MidrangeFrequencies

Human hearing is extremely sensitive at the 'high midrange' frequencies, with the slightest boost

around here resulting in a huge change in the sound timbre.

The 'high midrange' is responsible for the attack on percussive and rhythm instruments. If

boosted, this range can add presence. However, too much boost around the 3 kHz range can

cause listening fatigue. Vocals are most prominent at this range so as with the ‘midrange’, be

cautious when boosting.

Presence: 4 kHz to 6 kHz

Presence Frequencies

Cutting in this range makes sound more distant and transparent.

Brilliance: 6 kHz to 20 kHz

Brilliance Frequencies

The 'brilliance' range is composed entirely of harmonics and is responsible for sparkle and ‘air’

of a sound. Boost around 12 kHz make a recording sound more Hi Fi.

Over boosting in this region can accentuate hiss or cause ear fatigue.

Summary Table Of Frequency Ranges

Name Range Description

Sub-Bass 20 - 60 Hz Power, rumble

Bass 60 – 250 Hz Boom, thump, fat

Low-Midrange 250 – 500 Hz Full

Midrange 500 – 2000 Hz Horn , cheap

Upper-Midrange 2000 – 4000 Hz Prominent, Horn

Presence 4000 – 6000 Hz Clear, bright

Brilliance 6000 – 20, 000 Hz Air, sparkle

1.6 Signal power Units& volume units

Electronic noise is a random fluctuation in an electrical signal, a characteristic of

all electronic circuits. Noise generated by electronic devices varies greatly, as it can be produced

by several different effects. Thermal noise is unavoidable at non-zero temperature, while other

types depend mostly on device type or manufacturing quality and semiconductor defects (such as

conductance fluctuations, including 1/f noise).

In communication systems, the noise is an error or undesired random disturbance of a useful

information signal, introduced before or after the detector and decoder. The noise is a summation

of unwanted or disturbing energy from natural and sometimes man-made sources. Noise is,

however, typically distinguished from interference, (e.g. cross-talk, deliberate jamming or other

unwanted electromagnetic interference from specific transmitters), for example in the signal-to-

noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference

ratio (SNIR) measures. Noise is also typically distinguished from distortion, which is an

unwanted alteration of the signal waveform, for example in the signal-to-noise and distortion

ratio (SINAD). In a carrier-modulated passband analog communication system, a certain carrier-

to-noise ratio (CNR) at the radio receiver input would result in a certain signal-to-noise ratio in

the detected message signal. In a digital communications system, a certain Eb/N0 (normalized

signal-to-noise ratio) would result in a certain bit error rate (BER).

1.7 Summary

Analog signals are time varying voltages or currents that are continuously changing ,

such as sine and cosine waves. An analog signal contains an infinite number of values. Digital

signals are voltages or currents that change in discrete steps or levels. The most common form of

digital signal is binary, which has two levels. All forms of information, however, must be

converted to electromagnetic energy before being propagated through an electronic

communication system.

Contamination problems have become a major factor in determining the

manufacturability, quality, and reliability of electronic assemblies. Understanding the mechanics

and chemistry of contamination has become necessary for improving quality and reliability and

reducing costs of electronic assemblies. Electronic noise is a random fluctuation in an electrical

signal, a characteristic of all electronic circuits. Noise generated by electronic devices varies

greatly, as it can be produced by several different effects. The audio spectrum is the audible

frequency range at which humans can hear.

1.8 Keywords

• Electronic noise

• Power

• Audio spectrum

1.9 Exercise

1. Explain Contaminations.

2. Describe the Audio Spectrum.

3. Explain the Spectral Density of Thermal Noise

Unit 2

Electronic Communication System-2

Structure

2.1 Introduction

2.2 Objectives

2.3 Signal-to-noise-ratio

2.4 Analog and digital signals

2.5 Modulation

2.6 Fundamental Limitations In A Communication System

2.7Number System

2.8 Summary

2.9 Keywords

2.10 Exercise

2.1 Introduction

There are two types of signals that carry information - analog and digital signals. The

difference between analog and digital signals is that analog is a continuous electrical signal,

whereas digital is a non-continuous electrical signal.Modulation is the process of varying some

characteristic of a periodic wave with external signals. Modulation is utilized to send an

information bearing signal over long distances.Bandwidth is the information-carrying capacity of

a communication channel. The channel may be analog or digital.

2.2 Objectives


• Explain the Signal-to-noise-ratio

• Know Analog and digital signals

• Explain Modulation

• Know the Limitations In A Communication System

2.3 Signal-to-noise-ratio

The arch enemy of picture clarity on a monitor is noise, this is electronic noise that is

present to some extent in all video signals. Noise manifests itself as snow or graininess over the

whole picture on the monitor. There are several sources of noise; poor circuit design, heat, over-

amplification, external influences, automatic gain control, transmission systems such as

microwave, infrared etc. The important factor that determines the tolerance of noise is the

amount of noise in the video signal, the signal to noise ratio. Note that every time that a video

signal is processed in any way, noise is introduced.

The S/N ratio is exceedingly difficult to measure without special (and very expensive)

test equipment. For instance to test for S/N ratio could cost in the region of £25,000 for the

equipment. A less expensive way is to introduce a special filter to exclude the video signal and

measure the remaining noise, from which the S/N ratio can be calculated. However even this

filter can cost in the order of £1,000. Neither of these methods are practical in the field on actual

installations, even if the equipment could be afforded.

This leaves the problem that when viewing the picture on an installed system, the

assessment of the amount of noise is very subjective. One persons idea of a ‘noisy’ picture is not

necessarily anothers. The quality of the picture can also be aggravated by other factors as mains

hum, transmission losses, etc. These can be generally be overcome by isolation transformers,

video line correctors, using twisted pair transmission etc. However the noise cannot be reduced

by correction equipment, it is introduced at the source or in transmission systems. A common

source of noise is when automatic gain control (AGC) is introduced at a camera in very low light

conditions. This is why manufacturers state the minimum sensitivity of a camera with the

AGC on but the S/N ratio with AGC off.

The only real way to reduce noise lies in correct system design, selection of equipment and

transmission systems. Once it is there, it won’t go away and can only get worse.

Measuring S/N Ratio

There is though, one method of determining the S/N ratio which will give a reasonable guide.

The only equipment needed is an oscilloscope with a bandwidth of 10 MHz and a very sensitive

millivolt range. Connect the video signal to be checked to the ‘scope via a 75W impedance and

view the black level of the video signal. The black level should be at 0.3 volts which is the top of

the sync pulse. Normally this should be a thin horizontal line but when noise is present the line

will be thicker. Keep increasing the sensitivity of the millivolts reading until the thickness of the

line can be read to within 0.1 Mv. Note this reading in Mv, also the peak level of the video signal

above the black level i.e. the white level. The video signal is measured above the black level,

therefore if the black level is 0.3 v and the video white level is at 1.0 volts then the video signal

is

1.0-0.3=.07 v. Signal to noise ratios are calculated from the peak to peak value of the video

signal.

The signal to noise ratio is calculated as follows:

which for a 1volt p/p video signal becomes dB.

Where R is the signal to noise ratio and the signal and noise are measured in millivolts. The

signal to noise is actually based on the RMS value. Therefore, without going into theory, add

3dB to the calculated value. To calculate the noise level in millivolts from the above, the formula

can be transposed as below.

This gives the UNWEIGHTED value for the S/N ratio. When a filter is used to measure the S/N

ratio it gives a WEIGHTED value which is about 8dB greater than the unweighted value. Once

again many manufacturers do not state whether the value given is weighted or unweighted. It

seems safe to assume therefore that they will show the value that enhances the specification to

the maximum, which in this case would be the weighted value. If comparing different

specifications, it would be reasonable to deduct 8 dB from a weighted value to arrive at the

equivalent unweighted value.

In many cases the actual scene will not contain a great deal of black which can make it difficult

to determine the black level. In these situations try to focus on an area with a vertical contrast

between light and very dark areas. The best way, is to view a target made up with a vertical line

having a black surface on one side and a white surface on the other.

In most common cameras the signal to noise ratio will be in the order of 55 dB, i.e. a ratio of

562 : 1. That is, the signal is five hundred and sixty two times greater than the noise signal. At

this ratio the noise will be unnoticeable. The following guidelines interpret some ratios of signal

to noise in terms of the subjective picture quality. A S/N ratio of 46dB is generally accepted as

the threshold at which noise can be visually seen.

S/N ratio dB S/N ratio:1 Picture quality

60 dB 1,000 Excellent, no noise apparent

50 dB 316 Good, a small amount of noise but picture quality good.

40dB 100 Reasonable, fine grain or snow in the picture, some fine detail lost.

30 dB 32 Poor picture with a great deal of noise.

20 dB 10 Unusable picture.

Note that if the video signal is less than 1 volt p/p and the noise is constant, then the S/N ratio

will be less. (i.e. worse.) Some manufacturers specify the sensitivity of cameras using vague

terms, such as ‘usable video’, ‘50 IRE units’, ‘50% video signal’, etc. Using the camera at this

level of sensitivity will have an adverse affect on the S/N ratio.

To save calculation, some typical values are listed in the following table. The following graph

represents the relationship between signal to noise ratio in dB and the noise level in millivolts,

for a 1.0v p/p and a 0.5 volt p/p video signal. ( The values have been adjusted for the RMS value

of the noise measured.)

Graph showing the signal to noise ratios for 1 volt and 0.5 volt peak to peak video signal

2.4 Analog and digital signals

Instrumentation is a field of study and work centering on measurement and control of

physical processes. These physical processes include pressure, temperature, flow rate, and

chemical consistency. An instrument is a device that measures and/or acts to control any kind of

physical process. Due to the fact that electrical quantities of voltage and current are easy to

measure, manipulate, and transmit over long distances, they are widely used to represent such

physical variables and transmit the information to remote locations.

A signal is any kind of physical quantity that conveys information. Audible speech is certainly a

kind of signal, as it conveys the thoughts (information) of one person to another through the

physical medium of sound. Hand gestures are signals, too, conveying information by means of

light. This text is another kind of signal, interpreted by your English-trained mind as information

about electric circuits. In this chapter, the word signal will be used primarily in reference to an

electrical quantity of voltage or current that is used to represent or signify some other physical

quantity.

An analog signal is a kind of signal that is continuously variable, as opposed to having a limited

number of steps along its range (called digital). A well-known example of analog vs. digital is

that of clocks: analog being the type with pointers that slowly rotate around a circular scale, and

digital being the type with decimal number displays or a "second-hand" that jerks rather than

smoothly rotates. The analog clock has no physical limit to how finely it can display the time, as

its "hands" move in a smooth, pauseless fashion. The digital clock, on the other hand, cannot

convey any unit of time smaller than what its display will allow for. The type of clock with a

"second-hand" that jerks in 1-second intervals is a digital device with a minimum resolutionof

one second.

Both analog and digital signals find application in modern electronics, and the distinctions

between these two basic forms of information is something to be covered in much greater detail

later in this book. For now, I will limit the scope of this discussion to analog signals, since the

systems using them tend to be of simpler design.

With many physical quantities, especially electrical, analog variability is easy to come by. If

such a physical quantity is used as a signal medium, it will be able to represent variations of

information with almost unlimited resolution.

In the early days of industrial instrumentation, compressed air was used as a signaling medium to

convey information from measuring instruments to indicating and controlling devices located

remotely. The amount of air pressure corresponded to the magnitude of whatever variable was

being measured. Clean, dry air at approximately 20 pounds per square inch (PSI) was supplied

from an air compressor through tubing to the measuring instrument and was then regulated by

that instrument according to the quantity being measured to produce a corresponding output

signal. For example, a pneumatic (air signal) level "transmitter" device set up to measure height

of water (the "process variable") in a storage tank would output a low air pressure when the tank

was empty, a medium pressure when the tank was partially full, and a high pressure when the

tank was completely full.

The "water level indicator" (LI) is nothing more than a pressure gauge measuring the air pressure

in the pneumatic signal line. This air pressure, being a signal, is in turn a representation of the

water level in the tank. Any variation of level in the tank can be represented by an appropriate

variation in the pressure of the pneumatic signal. Aside from certain practical limits imposed by

the mechanics of air pressure devices, this pneumatic signal is infinitely variable, able to

represent any degree of change in the water's level, and is therefore analog in the truest sense of

the word.

Crude as it may appear, this kind of pneumatic signaling system formed the backbone of many

industrial measurement and control systems around the world, and still sees use today due to its

simplicity, safety, and reliability. Air pressure signals are easily transmitted through inexpensive

tubes, easily measured (with mechanical pressure gauges), and are easily manipulated by

mechanical devices using bellows, diaphragms, valves, and other pneumatic devices. Air

pressure signals are not only useful for measuring physical processes, but for controlling them as

well. With a large enough piston or diaphragm, a small air pressure signal can be used to

generate a large mechanical force, which can be used to move a valve or other controlling

device. Complete automatic control systems have been made using air pressure as the signal

medium. They are simple, reliable, and relatively easy to understand. However, the practical

limits for air pressure signal accuracy can be too limiting in some cases, especially when the

compressed air is not clean and dry, and when the possibility for tubing leaks exist.

With the advent of solid-state electronic amplifiers and other technological advances, electrical

quantities of voltage and current became practical for use as analog instrument signaling media.

Instead of using pneumatic pressure signals to relay information about the fullness of a water

storage tank, electrical signals could relay that same information over thin wires (instead of

tubing) and not require the support of such expensive equipment as air compressors to operate:

Analog electronic signals are still the primary kinds of signals used in the instrumentation world

today (January of 2001), but it is giving way to digital modes of communication in many

applications (more on that subject later). Despite changes in technology, it is always good to

have a thorough understanding of fundamental principles, so the following information will

never really become obsolete.

One important concept applied in many analog instrumentation signal systems is that of "live

zero," a standard way of scaling a signal so that an indication of 0 percent can be discriminated

from the status of a "dead" system. Take the pneumatic signal system as an example: if the signal

pressure range for transmitter and indicator was designed to be 0 to 12 PSI, with 0 PSI

representing 0 percent of process measurement and 12 PSI representing 100 percent, a received

signal of 0 percent could be a legitimate reading of 0 percent measurement or it could mean that

the system was malfunctioning (air compressor stopped, tubing broken, transmitter

malfunctioning, etc.). With the 0 percent point represented by 0 PSI, there would be no easy way

to distinguish one from the other.

If, however, we were to scale the instruments (transmitter and indicator) to use a scale of 3 to 15

PSI, with 3 PSI representing 0 percent and 15 PSI representing 100 percent, any kind of a

malfunction resulting in zero air pressure at the indicator would generate a reading of -25 percent

(0 PSI), which is clearly a faulty value. The person looking at the indicator would then be able to

immediately tell that something was wrong.

Not all signal standards have been set up with live zero baselines, but the more robust signals

standards (3-15 PSI, 4-20 mA) have, and for good reason.

2.5 Modulation

Modulation is the process where a Radio Frequency or Light Wave's amplitude,

frequency, or phase is changed in order to transmit intelligence. The characteristics of the carrier

wave are instantaneously varied by another "modulating" waveform.

There are many ways to modulate a signal:

• Amplitude Modulation

• Frequency Modulation

• Phase Modulation

• Pulse Modulation

Additionally, digital signals usually require an intermediate modulation step for transport across

wideband, analog-oriented networks.

Amplitude Modulation (AM)

Amplitude Modulation occurs when a voice signal's varying voltage is applied to a carrier

frequency. The carrier frequency's amplitude changes in accordance with the modulated voice

signal, while the carrier's frequency does not change.

When combined the resultant AM signal consists of the carrier frequency, plus UPPER and

LOWER sidebands. This is known as Double Sideband - Amplitude Modulation (DSB-AM), or

more commonly referred to as plain AM.

The carrier frequency may be suppressed or transmitted at a relatively low level. This requires

that the carrier frequency be generated, or otherwise derived, at the receiving site for

demultiplexing. This type of transmission is known as Double Sideband - Suppressed Carrier

(DSB-SC).

It is also possible to transmit a SINGLE sideband for a slight sacrifice in low frequency response

(it is difficult to suppress the carrier and the unwanted sideband, without some low frequency

filtering as well). The advantage is a reduction in analog bandwidth needed to transmit the

signal. This type of modulation, known as Single Sideband - Suppressed Carrier (SSB-SC), is

ideal for Frequency Division Multiplexing (FDM).

Another type of analog modulation is known as Vestigial Sideband. Vestigial Sideband

modulation is a lot like Single Sideband, except that the carrier frequency is preserved and one of

the sidebands is eliminated through filtering. Analog bandwidth requirements are a little more

than Single Sideband however.

Vestigial Sideband transmission is usually found in television broadcasting. Such broadcast

channels require 6 MHz of ANALOG bandwidth, in which an Amplitude Modulated PICTURE

carrier is transmitted along with a Frequency Modulated SOUND carrier.

Frequency Modulation (FM)

Frequency Modulation occurs when a carrier's CENTER frequency is changed based upon the

input signal's amplitude. Unlike Amplitude Modulation, the carrier signal's amplitude is

UNCHANGED. This makes FM modulation more immune to noise than AM and improves the

overall signal-to-noise ratio of the communications system. Power output is also constant,

differing from the varying AM power output.

The amount of analog bandwidth necessary to transmit a FM signal is greater than the amount

necessary for AM, a limiting constraint for some systems.

Phase Modulation

Phase Modulation is similar to Frequency Modulation. Instead of the frequency of the carrier

wave changing, the PHASE of the carrier changes.

As you might imagine, this type of modulation is easily adaptable to data modulation

applications.

Pulse Modulation (PM)

With Pulse Modulation, a "snapshot" (sample) of the waveform is taken at regular intervals.

There are a variety of Pulse Modulation schemes:

• Pulse Amplitude Modulation

• Pulse Code Modulation

• Pulse Frequency Modulation

• Pulse Position Modulation

• Pulse Width Modulation

Pulse Amplitude Modulation (PAM)

In Pulse Amplitude Modulation, a pulse is generated with an amplitude corresponding to that of

the modulating waveform. Like AM, it is very sensitive to noise.

While PAM was deployed in early AT&T Dimension PBXs, there are no practical

implementations in use today. However, PAM is an important first step in a modulation scheme

known as Pulse Code Modulation.

Pulse Code Modulation (PCM)

In Pulse Code Modulation, PAM samples (collected at regular intervals) are quantized. That is to

say, the amplitude of the PAM pulse is assigned a digital value (number). This number is

transmitted to a receiver that decodes the digital value and outputs the appropriate analog pulse.

The fidelity of this modulation scheme depends upon the number of bits used to represent the

amplitude. The frequency range that can be represented through PCM modulation depends upon

the sample rate. To prevent a condition known as "aliasing", the sample rate MUST BE AT

LEAST twice that of the highest supported frequency. For typical voice channels (4 Khz

frequency range), the sample rate is 8 KHz.

Where is PCM today? Well, its EVERYWHERE! A typical PCM voice channel today operates

at 64 KBPS (8 bits/sample * 8000 samples/sec). But other PCM schemes are widely deployed in

today's audio (CD/DAT) and video systems!

Pulse Frequency Modulation (PFM)

With PFM, pulses of equal amplitude are generated at a rate modulated by the signal's frequency.

The random arrival rate of pulses makes this unsuitable for transmission through Time Division

Multiplexing (TDM) systems.

Pulse Position Modulation (PPM)

Also known as Pulse Time Modulation, PPM is a scheme where the pulses of equal amplitude

are generated at a rate controlled by the modulating signal's amplitude. Again, the random arrival

rate of pulses makes this unsuitable for transmission using TDM techniques.

Pulse Width Modulation (PWM)

In PWM, pulses are generated at a regular rate. The length of the pulse is controlled by the

modulating signal's amplitude. PWM is unsuitable for TDM transmission due to the varying

pulse width.

Digital Signal Modulation

Digital signals need to be processed by an intermediate stage for conversion into analog signals

for transmission. The device that accomplishes this conversion is known as a "Modem"

(MODulator/DEModulator).

2.6 Fundamental Limitations In A Communication System

The Fundamental Limitations In A Communication System are

• Noise

• Bandwidth

Noise

In communication systems, the noise is an error or undesired random disturbance of a useful

information signal, introduced before or after the detector and decoder. The noise is a summation

of unwanted or disturbing energy from natural and sometimes man-made sources. Noise is,

however, typically distinguished from interference, (e.g. cross-talk, deliberate jamming or other

unwanted electromagnetic interference from specific transmitters), for example in the signal-to-

noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference

ratio (SNIR) measures. Noise is also typically distinguished from distortion, which is an

unwanted alteration of the signal waveform, for example in the signal-to-noise and distortion

ratio (SINAD). In a carrier-modulated passband analog communication system, a certain carrier-

to-noise ratio (CNR) at the radio receiver input would result in a certain signal-to-noise ratio in

the detected message signal. In a digital communications system, a certain Eb/N0 (normalized

signal-to-noise ratio) would result in a certain bit error rate (BER).

Bandwidth

Bandwidth is the information-carrying capacity of a communication channel. The channel may

be analog or digital. Analog transmissions such as telephone calls, AM and FM radio, and

television are measured in cycles per second (hertz or Hz). Digital transmissions are measured in

bits per second. For digital systems, the terms "bandwidth" and "capacity" are often used

interchangeably, and the actual transmission capabilities are referred to as the data transfer rate

(or just data rate).

2.7 Number System

This section will introduce some basic number system concepts and introduce number systems

useful in electrical and computer engineering.

The decimal number system

In childhood, people are often taught the fundamentals of counting by using their fingers.

Counting from one to ten is one of many milestones a child achieves on their way to becoming

educated members of society. We will review these basic facts on our way to gaining an

understanding of alternate number systems.

The child is taught that the fingers and thumbs can be used to count from one to ten. Extending

one finger represents a count of one; two fingers represents a count of two, and so on up to a

maximum count of ten. No fingers (or thumbs) refers to a count of zero.

The child is later taught that there are certain symbols called digits that can be used to represent

these counts. These digits are, of course:

Ten, of course, is a special case, since it is comprised of two digits.

Before we go deeper, we need a few fundamental definitions.

Digit

A digit is a symbol given to an element of a number system.

Radix

The radix, or base of a counting system is defined as the number of unique digits in a given

number system.

Back to our elementary example. We know that our hypothetical child can count from zero to ten

using their fingers and thumbs. There are ten unique digits in this counting system, therefore the

radix of our elementary counting system is ten.

We represent the radix of our counting system by putting the radix in subscript to the right of the

digits. For example,

represents 3 in decimal (base 10).

Our special case (ten) illustrates a fundamental rule of our number system that was not readily

apparent - what happens when the count exceeds the highest digit? Obviously, a new digit is

added, to the left of our original digit which is "worth more", or has a higher weight than our

original digit. (In reality, there *always* are digits to the left; we simply choose not to write

those digits to the left of the first nonzero.)

When our count exceeds the highest digit available, the next digit to the left is incremented and

the original digit is reset to zero. For example:

Because we are dealing with a base-10 system, each digit to the left of another digit is weighted

ten times higher. Using exponential notation, we can imagine the number 10 as representing:

The fundamentals of decimal arithmetic will not be expanded on in this lecture.

The binary number system

It is widely believed that the decimal system that we find so natural to use is a direct

consequence of a human being's ten fingers and thumbs being used for counting purposes. One

could easily imagine that a race of intelligent, six-fingered beings could quite possibly have

developed a base-six counting system. From this perspective, consider the hypothesis: the most

intuitive number system for an entity is that for which some natural means of counting exists.

Since our focus is electronic and computer sys

hand to the switch, arguably the most fundamental structure that can be used to represent a count.

The switch can represent one of two states;

definition of a digit, how many digits are required to represent the possible states of our switch?

Clearly, the answer is 2. We use the binary digits zero and one to represent the open and closed

states of the switch.

Bits and bytes

A bit is a digit in the binary counting system.

A nybble (also spelled nibble) is a binary number co

A byte, or octet is a binary number consisting of eight bits.

From our earlier definition of radix, the binary

subscript much like we do with decimals:

Counting

Similar to decimals, binary digits are weighted. Each bit is weighted twice as much as the bit to

the right of it:

Counting from one to ten (base 10) i

Basic binary arithmetic

Binary addition, subtraction, multiplication and division operations work essentially the same as

they do for decimals.

six counting system. From this perspective, consider the hypothesis: the most


Since our focus is electronic and computer systems, we must narrow our focus from the human

, arguably the most fundamental structure that can be used to represent a count.

The switch can represent one of two states; either open, or closed. If we return to our original



is a digit in the binary counting system.

(also spelled nibble) is a binary number consisting of four bits.

is a binary number consisting of eight bits.

From our earlier definition of radix, the binary system has a radix of two. We use the radix in the

subscript much like we do with decimals:


Counting from one to ten (base 10) in binary yields:


six counting system. From this perspective, consider the hypothesis: the most


tems, we must narrow our focus from the human

, arguably the most fundamental structure that can be used to represent a count.

either open, or closed. If we return to our original



system has a radix of two. We use the radix in the



For addition, you add equally-weighted bits, much like decimal addition (where you add equal

weighted digits) and carry as required to the left.

As you can see, a carry is generated in the

Subtraction works just like decimal arithmetic, using borrowing as required.

Here, a borrow is required, reducing

to .

Multiplication is straightforward also:

Division is left as an exercise to the student [hint: use long division].

Conversion between binary and decimal

When you consider a binary number in exponential

conversion:

...simply add up the factors.

weighted bits, much like decimal addition (where you add equal

weighted digits) and carry as required to the left.

As you can see, a carry is generated in the column which increments the column.

Subtraction works just like decimal arithmetic, using borrowing as required.

Here, a borrow is required, reducing the column to and changing the

Multiplication is straightforward also:

Division is left as an exercise to the student [hint: use long division].

Conversion between binary and decimal

When you consider a binary number in exponential form, you can easily perform a decimal

weighted bits, much like decimal addition (where you add equally-

column.

and changing the column

form, you can easily perform a decimal

To convert from decimal to binary, you can repeatedly divide the decimal by two until the result

of the division is zero. Starting from the rightmost bit, write 1 if the division has a remainder,

zero if it does not. For example, to convert the decimal 74 into binary:

* 74 / 2 = 37 remainder 0; -> 0

* 37 / 2 = 18 remainder 1; -> 10

* 18 / 2 = 9 remainder 0; -> 010

* 9 / 2 = 4 remainder 1; -> 1010

* 4 / 2 = 1 remainder 0; -> 01010

* 2 / 2 = 1 remainder 0; -> 001010

* 1 / 2 = 0 remainder 1; -> 1001010

The octal number system

The name octal implies eight, if you consider that an octagon has eight sides. Octal has a radix of

eight, and uses the following octal digits:

An octal number has the subscript 8.

Counting

Counting from one to ten (base 10) in octal yields:

Octal arithmetic

Octal arithmetic, like binary arithmetic, follows the same rules and patterns of decimal

arithmetic. As an exercise, verify the following:

Conversion between binary and octal

Each octal digit is representable by exactly three bits. This becomes obvious when you consider

that the highest octal digit is seven, which can be represented in binary by

To convert a binary number to octal, group the bits in groups of three starting from the rightmost

bit and convert each triplet to its octal equivalent.

To convert an octal number to binary, simply wr

Conversion from decimal to octal

The repeated-division method described for binary will also work for octal, simply by changing

the divisor to eight. To convert 67 (base 10 into octal):

* 67 / 8 = 8 remainder 3; -> 3

* 8 / 8 = 1 remainder 0; -> 03

* 1 / 8 = 0 remainder 1; -> 103

The hexadecimal number system

The most commonly-used number system in computer systems is the

simply hex, system. It has a radix of 16, and uses the numbers zero through nine, as well as A

through F as its digits:

Hex numbers can have the subscript 16, bu

type.

Conversion between binary and octal


it is seven, which can be represented in binary by .


bit and convert each triplet to its octal equivalent.

To convert an octal number to binary, simply write the equivalent bits for each octal number.

Conversion from decimal to octal

division method described for binary will also work for octal, simply by changing

the divisor to eight. To convert 67 (base 10 into octal):

> 3

> 03

> 103

The hexadecimal number system

used number system in computer systems is the hexadecimal


Hex numbers can have the subscript 16, but more often have a leading *0x* to indicate their


.


ite the equivalent bits for each octal number.

division method described for binary will also work for octal, simply by changing

hexadecimal, or more


t more often have a leading *0x* to indicate their

Counting

Counting from zero to twenty (base 10) in hex yields:

Hexadecimal arithmetic

Hex arithmetic, yet again, follows the same rules and patterns of decimal arithmetic. As an

exercise, verify the following:

Conversion between hexadecimal and binary

Each hex digit is representable by exactly four bits. This becomes obvious when you consider

that the highest hex digit represents fifteen, which can be represented in binary by

To convert a binary number to hex, group the bits in groups of four starting from the rightmost

bit and convert each group to its hex equivalent.

To convert an hex number to binary, simply write the equivalent bits for each hex number.

Representing Logic States

high 1 or on

Counting from zero to twenty (base 10) in hex yields:


Conversion between hexadecimal and binary


that the highest hex digit represents fifteen, which can be represented in binary by

a binary number to hex, group the bits in groups of four starting from the rightmost

bit and convert each group to its hex equivalent.


low 0 or off



that the highest hex digit represents fifteen, which can be represented in binary by .

a binary number to hex, group the bits in groups of four starting from the rightmost


X

100M

X 100K

X 100

X 100m

X 100µ

Ω

A

DC

AC

C L

X

100M

X 100K

X 100

X 100m

X 100µ

Ω

A

DC

AC

C L

VCC to Vhigh in = logic high

vlow in to gnd = logic low

technology CMOS TTL/CMOS TTL LVTTL LVCMOS

technology

type

AC, HC,

AHC, H

ACT, HCT, AHCT,

FCT

F, S, AS, LS,

ALS LV

LV, LVC,

ALVC

vcc 5v 5v 5v-4.5v 3.6v-3v 3.6v-3v

vhigh Out 4.7v 4.7v 3.3v or 2.4v 2.4v 3.5v

vhigh In Min 3.7v 2.0v 2.0v 2.0v 2.6v

transition

vlow In Max 1.3v .8v .8v .8v .72v

vlow Out .2v .2v .35v .4v .54v

Most 5v logic will have no problem with a 5V high or a 0V low. You should always refer to the

data sheet before choosing your device.

2.8 Summary

A signal is any kind of detectable quantity used to communicate

information.An analog signal is a signal that can be continuously, or infinitely, varied to

represent any small amount of change.Pneumatic, or air pressure, signals used to be used

predominately in industrial instrumentation signal systems. This has been largely superseded

by analog electrical signals such as voltage and current.A live zero refers to an analog signal

scale using a non-zero quantity to represent 0 percent of real-world measurement, so that any

system malfunction resulting in a natural "rest" state of zero signal pressure, voltage, or

current can be immediately recognized.Modulation is the process of varying some

characteristic of a periodic wave with external signals.Modulation is utilized to send an

information bearing signal over long distances.Bandwidth is the information-carrying

capacity of a communication channel. The channel may be analog or digital.

2.9 Keywords

• Ratio

• WEIGHTED

• Modulation

• AM

• FM

• Phase Modulation

• PM

• PAM

• PCM

• PFM

• PPM

• PWM

2.10 Exercise

1 Explain the Signal-to-noise-ratio.

2 Differentiate Analog and digital signals.

3 Explain Modulation.

4 Convert the following binary numbers to decimal:

5 Convert the following decimal numbers to binary:

6 Add the following numbers:

Unit 3

SAMPLING AND ANALOG PULSE MODULATION-1

Structure

3.1 Introduction

3.2 Objectives

3.3 Sampling Theory

3.4 Sampling Analysis

3.5 Types of sampling

3.6 Summary

3.7 Keywords

3.8 Exercise

3.1 Introduction

In signal processing, sampling is the reduction of a continuous signal to a discrete signal.

A common example is the conversion of a sound wave (a continuous signal) to a sequence of

samples (a discrete-time signal).

A sample refers to a value or set of values at a point in time and/or space.

A sampler is a subsystem or operation that extracts samples from a continuous signal. A

theoretical ideal sampler produces samples equivalent to the instantaneous value of the

continuous signal at the desired points.

3.2 Objectives

After studying this unit we are able to understand

− Sampling Theory

− Sampling Analysis

− Types of sampling

3.3 Sampling Theory

Sampling theory is derived as an application of the DTFT and the Fourier

theorems developed in Appendix C. First, we must derive a formula for aliasing due to

uniformly sampling a continuous-time signal. Next, the sampling theorem is proved. The

sampling theorem provides that a properly bandlimited continuous-time signal can be sampled

and reconstructed from its samples without error, in principle.

An early derivation of the sampling theorem is often cited as a 1928 paper by Harold Nyquist,

and Claude Shannon is credited with reviving interest in the sampling theorem after World War

II when computers became public.D.1As a result, the sampling theorem is often called ``Nyquist's

sampling theorem,'' ``Shannon's sampling theorem,'' or the like. Also, the sampling rate has been

called the Nyquist rate in honor of Nyquist's contributions [48]. In the author's experience,

however, modern usage of the term ``Nyquist rate'' refers instead to half the sampling rate. To

resolve this clash between historical and current usage, the term Nyquist limit will always

mean half the sampling rate in this book series, and the term ``Nyquist rate'' will not be used at

all.

3.4 Sampling Analysis

Sampling a continuous time signal produces a discrete time signal by selecting the values of the

continuous time signal at evenly spaced points in time. Thus, sampling a continuous time

signal x with sampling period Ts gives the discrete time signal xs defined by xs(n)=x(nTs). The

sampling angular frequency is then given by ωs=2π/Ts.

It should be intuitively clear that multiple continuous time signals sampled at the same rate can

produce the same discrete time signal since uncountably many continuous time functions could

be constructed that connect the points on the graph of any discrete time function. Thus, sampling

at a given rate does not result in an injective relationship. Hence, sampling is, in general, not

invertible.

EXAMPLE 1

For instance, consider the signals x,y defined by

x(t)=sin(t)t(1)

y(t)=sin(5t)t(2)

and their sampled versions xS,ys with sampling period Ts=π/2

xs(n)=sin(nπ/2)nπ/2(3)

ys(n)=sin(n5π/2)nπ/2.(4)

Notice that since

sin(n5π/2)=sin(n2π+nπ/2)=sin(nπ/2)(5)

it follows that

ys(n)=sin(nπ/2)nπ/2=xs(n).(6)

Hence, x and y provide an example of distinct functions with the same sampled versions at a

specific sampling rate.

It is also useful to consider the relationship between the frequency domain representations of the

continuous time function and its sampled versions. Consider a signal x sampled with sampling

period Ts to produce the discrete time signal xs(n)=x(nTs). The

spectrum Xs(ω) for ω∈[−π,π) of xs is given by

Xs(ω)=∑n=−∞∞x(nTs)e−jωn.(7)

Using the continuous time Fourier transform, x(tTs) can be represented as

x(tTs)=12πTs∫∞−∞X(ω1Ts)ejω1tdω1.(8)

Thus, the unit sampling period version of x(tTs), which is x(nTs) can be represented as

x(nTs)=12πTs∫∞−∞X(ω1Ts)ejω1ndω1.(9)

This is algebraically equivalent to the representation

x(nTs)=1Ts∑k=−∞∞12π∫π−πX(ω1−2πkTs)ej(ω1−2πk)ndω1,(10)

which reduces by periodicity of complex exponentials to

x(nTs)=1Ts∑k=−∞∞12π∫π−πX(ω1−2πkTs)ejω1ndω1.(11)

Hence, it follows that

Xs(ω)=1Ts∑k=−∞∞∑n=−∞∞(∫π−πX(ω1−2πkTs)ejω1ndω1)e−jωn.(12)

Noting that the above expression contains a Fourier series and inverse Fourier series pair, it

follows that

Xs(ω)=1Ts∑k=−∞∞X(ω−2πkTs).(13)

Hence, the spectrum of the sampled signal is, intuitively, the scaled sum of an infinite number of

shifted and time scaled copies of original signal spectrum. Aliasing, which will be discussed in

depth in later modules, occurs when these shifted spectrum copies overlap and sum together.

Note that when the original signal x is bandlimited to (−π/Ts,π/Ts) no overlap occurs, so each

period of the sampled signal spectrum has the same form as the orignal signal spectrum. This

suggest that if we sample a bandlimited signal at a sufficiently high sampling rate, we can

recover it from its samples as will be further described in the modules on the Nyquist-Shannon

sampling theorem and on perfect reconstruction.

3.5 Types of sampling

The various types of sampling, PCM, DM, DPCM etc

pulse code modulation (PCM)

Pulse code modulation (PCM) is a digital scheme for transmitting analogdata. The signals in

PCM are binary; that is, there are only two possible states, represented by logic 1 (high) and

logic0 (low). This is true no matter how complex the analog waveform happens to be. Using

PCM, it is possible to digitize all forms of analog data, including full-motion video, voices,

music, telemetry, and virtual reality (VR).

To obtain PCM from an analog waveform at the source (transmitter end) of a communications

circuit, the analog signal amplitude is sampled (measured) at regular time intervals.The sampling

rate, or number of samples per second, is several times the maximum frequency of the analog

waveform in cycles per second or hertz. The instantaneous amplitude of the analog signal at each

sampling is rounded off to the nearest of several specific, predetermined levels. This process is

called quantization. The number of levels is always a power of 2 -- for example, 8, 16, 32, or 64.

These numbers can be represented by three, four, five, or six binary digits (bits)respectively. The

output of a pulse code modulator is thus a series of binary numbers, each represented by some

power of 2bits.

At the destination (receiver end) of the communications circuit, a pulse code demodulator

converts the binary numbers back into pulses having the same quantum levels as those in the

modulator. These pulses are further processed to restore the original analog waveform.

Modulation

Modulation is the addition of information (or the signal) to an electronic or optical signal carrier.

Modulation can be applied to direct current (mainly by turning it on and off), to alternating

current, and to optical signals. One can think of blanket waving as a form of modulation used in

smoke signal transmission (the carrier being a steady stream of smoke).Morse code, invented for

telegraphy and still used in amateur radio, uses a binary (two-state) digital code similar to the

code used by modern computers. For most of radio and telecommunication today, the carrier is

alternating current (AC) in a given range of frequencies. Common modulation methods include:

Amplitude modulation (AM), in which the voltage applied to the carrier is varied over

time

Frequency modulation (FM), in which the frequency of the carrier waveform is varied in

small but meaningful amounts

Phase modulation (PM), in which the natural flow of the alternating current waveform

is delayed temporarily

These are sometimes known as continuous wave modulation methods to distinguish them from

pulse code modulation (PCM), which is used to encode both digital and analog information in a

binary way. Radio and television broadcaststations typically use AM or FM. Most two-way

radios use FM, although some employ a mode known as single sideband (SSB).

More complex forms of modulation are Phase Shift Keying (PSK) and Quadrature Amplitude

Modulation (QAM). Optical signals are modulated by applying an electromagnetic current to

vary the intensity of a laser beam.

Modem Modulation and Demodulation

A computer with an online or Internet connection that connects over a regular analog phone line

includes a modem. This term is derived by combining beginning letters from the words

modulator and demodulator. In a modem, the modulation process involves the conversion of the

digital computer signals (high and low, or logic 1 and 0 states) to analog audio-frequency

(AF)tones. Digital highs are converted to a tone having a certain constant pitch; digital lows are

converted to a tone having a different constant pitch. These states alternate so rapidly that,if you

listen to the output of a computer modem, it sounds like a hiss or roar. The demodulation process

converts the audio tones back into digital signals that a computer can understand. directly.

Multiplexing

More information can be conveyed in a given amount of time by dividing the bandwidth of a

signal carrier so that more than one modulated signal is sent on the same carrier. Known as

multiplexing, the carrier is sometimes referred to as a channel and each separate signal carried on

it is called a subchannel. (In some usages, each subchannel is known as a channel.) The device

that puts the separate signals on the carrier and takes them off of received transmissions is a

multiplexer. Common types of multiplexing include frequency-division multiplexing (FDM) and

time-division multiplexing (TDM). FDM is usually used for analog communication and divides

the main frequency of the carrier into separate subchannels, each with its own frequency band

within the overall bandwidth. TDM is used for digital communication and divides the main

signal into time-slots, with each time-slot carrying a separate signal.

Delta modulation and DPCM

PCM is powerful, but quite complex coders and decoders are required. An increase in resolution

also requires a higher number of bits per sample. Standard PCM systems have no memory —

each sample value is separately encoded into a series of binary digits. An alternative, which

overcomes some limitations of PCM is to use past information in the encoding process. One way

of doing this is to perform source coding using delta modulation:

The signal is first quantised into discrete levels, but the size of the s

is kept constant. The signal may therefore only make a transition from one level to an adjacent

one. Once the quantisation operation is performed, transmission of the signal can be achieved by

sending a zero for a negative tran

that the quantised signal must change at each sampling point.

For the above case, the transmitted bit train would be 111100010111110. The

demodulator for a delta-modulated signal is simply a

staircase increments positively, and if a zero is received, negatively. This is usually followed by

a lowpass filter. The key to using delta modulation is to make the right choice of step size and

sampling period — an incorrect selection will mean that the signal changes too fast for the steps

to follow, a situation called overloading. Important parameters are therefore the step size and the

sampling period.

first quantised into discrete levels, but the size of the step between adjacent samples



sending a zero for a negative transition, and a one for a positive transition. Note that this means



modulated signal is simply a staircase generator. If a one is received, the


filter. The key to using delta modulation is to make the right choice of step size and

an incorrect selection will mean that the signal changes too fast for the steps


tep between adjacent samples



sition, and a one for a positive transition. Note that this means


staircase generator. If a one is received, the


filter. The key to using delta modulation is to make the right choice of step size and

an incorrect selection will mean that the signal changes too fast for the steps


If the signal has a known upper

which it can change. Assuming that the signal is

, the maximum slope is given by

For a DM system with step size a, the maximum rate of rise that can be handled is

a/Ts= afs, so we require

Making the assumption that the quantisation noise in DM is uniformly distributed over (

the mean-square quantisation error power is a

over all frequencies up to the sampling frequency fs . However, the

the DM receiver — if the cutoff frequency is set to the maximum frequency fm , then the total

noise power in the reconstructed signal is

Still making the assumption of a sinusoidal signal, the SNR for DM is

when the slope overload condition is just met. The SNR therefore increases by 9dB for every

doubling of the sampling frequency. Delta modulation is extremely simple, and gives acceptible

performance in many applications, but is clearly limited. One way of attempting

performance is to use adaptive DM, where the step size is not required to be constant. (The voice

If the signal has a known upper-frequency cutoff ψm , then we can estimate thefastest rate at


the maximum slope is given by


Making the assumption that the quantisation noise in DM is uniformly distributed over (

square quantisation error power is a2/3. We assume that this power is spread evenly

over all frequencies up to the sampling frequency fs . However, there is still the lowpass

if the cutoff frequency is set to the maximum frequency fm , then the total

noise power in the reconstructed signal is


ope overload condition is just met. The SNR therefore increases by 9dB for every


performance in many applications, but is clearly limited. One way of attempting


m , then we can estimate thefastest rate at


Making the assumption that the quantisation noise in DM is uniformly distributed over (-a,.a),

/3. We assume that this power is spread evenly

re is still the lowpass filter in

if the cutoff frequency is set to the maximum frequency fm , then the total

ope overload condition is just met. The SNR therefore increases by 9dB for every


performance in many applications, but is clearly limited. One way of attempting to improve


communication systems on the US space shuttles make use of this technique.) Another is to use

delta PCM, where each desired step

size is encoded as a (multiple bit) PCM signal, and transmitted to the receiver as a code word.

Differential PCM is similar, but encodes the difference between a sample and its predicted value

— this can further reduce the number of bits required for transmission.

ADPCM

Short for Adaptive Differential Pulse Code Modulation, a form of pulse code modulation

(PCM) that produces a digital signal with a lower bit rate than standard PCM. ADPCM produces

a lower bit rate by recording only the difference between samples and adjusting the coding scale

dynamically to accommodate large and small differences. Some applications use ADPCM

todigitize a voice signal so voice and data can be transmitted simultaneously over a digital

facility normally used only for one or the other. Adaptive DPCM (ADPCM) is a variant

of DPCM (differential pulse-code modulation) that varies the size of the quantization step, to

allow further reduction of the required bandwidth for a given signal-to-noise ratio.Typically, the

adaptation to signal statistics in ADPCM consists simply of an adaptive scale factor before

quantizing the difference in the DPCM encoder.

3.6 Summary

Sampling a continuous time signal produces a discrete time signal by selecting the values

of the continuous time signal at equally spaced points in time. However, we have shown that this

relationship is not injective as multiple continuous time signals can be sampled at the same rate

to produce the same discrete time signal. This is related to a phenomenon called aliasing which

will be discussed in later modules. Consequently, the sampling process is not, in general,

invertible. Nevertheless, as will be shown in the module concerning reconstruction, the

continuous time signal can be recovered from its sampled version if some additional assumptions

hold.

PCM: The analog speech waveform is sampled and converted directly into a multibit

digital code by an A/D converter. The code is stored and subsequently recalled for

playback

DM: Only a single bit is stored for each sample. This bit 1 or 0, represents a greater than

or less than condition, respectively as compared to the previous sample. An integrator is

then used on the output to convert the stored nit stream to an analog signal.

DPCM: Stores a multibit difference value. A bipolar D/A converter is used for playback

to convert the successive difference values to an analog waveform.

ADPCM: Stores a difference value that has been mathematically adjusted according to

the slope of the input waveform. Bipolar D/A converter is used to convert the stored

digital code to analog for playback.

3.7 Keywords

PCM

DM

DPCM

ADPCM

3.8 Exercise

1. Give the full name of PCM, DM, DPCM and ADPCM. Describe their fundamental

differences.

2. Explain the sampling theory

3. Explain sampling analysis

4. What are different types of sampling?

Unit 4

SAMPLING AND ANALOG PULSE MODULATION-2

Structure

4.1 Introduction

4.2 Objectives

4.3 Types Of Analog Pulse modulation

4.4 Pulse-Amplitude Modulation (PAM)

4.5 Analog Pulse Density Modulation (PDM)

4.6 Analog Pulse Width Modulation

4.7 Pulse-position modulation (PPM)

4.8 Signal-To-Noise Ratios In Pulse Systems

4.9 Summary

4.10 Keywords

4.11 Exercise

4.1 Introduction

This chapter is dedicated to analog pulse modulation characterized by the use of an

analogreference input to the pulse modulator. It is attempted to devise modulation strategies

thatwill lead to the optimal PMA performance. This is carried out by a fundamental review

andcomparison of known pulse modulation methods, followed by investigations of newenhanced

pulse modulation methods with improved characteristics. The analysis is basedon the derivation

of Double Fourier Series (DFS) expressions for all considered methods,and the introduction for a

spectral analysis tool – the Harmonic Envelope Surface (HES) –based on the analytical DFS

expressions. The HES offers detailed insight in the (for PMAs)interesting aspects and the tool

proves indispensable of a coherent analysis and comparisonof extensive set of pulse modulation

methods that are investigated throughout this centralchapter. A new multi-level modulation

method – Phase Shifted Carrier Pulse WidthModulation (PSCPWM) [Ni97b] – is introduced and

subjected to a detailed investigation.A suite of PSCPWM methods are defined each with distinct

characteristics, and it willappear that the principle provides optimal pulse modulation for PMAs

from a theoreticalpoint of view.

4.2 Objectives

After studying this unit we are able to understand

− Types of Analog Pulse modulation

− Pulse-Amplitude Modulation (PAM)

− Analog Pulse Density Modulation (PDM)

− Analog Pulse Width Modulation

− Pulse-position modulation (PPM)

− Signal-To-Noise Ratios In Pulse Systems

4.3 Types Of Analog Pulse modulation

Pulse modulation systems represent a message-bearing signal by a train of pulses. The

fourbasic pulse modulation techniques are [Bl53] Pulse Amplitude Modulation (PAM),

PulseWidth Modulation (PWM), Pulse Position modulation (PPM) and Pulse Density

Fig. 4.1 Fundamental pulse modulation methods

Modulation (PDM). Fig. 4.1 illustrates these four fundamental principles of analog

pulsemodulation. Pulse Amplitude Modulation (PAM) is based on a conversion the signal into

aseries of amplitude-modulated puls

given by the Nyquist sampling theorem, so the modulated signal can be uniquelyrepresented by

uniformly spaced samples of the signal at a rate higher or equal to two timesthe signal

bandwidth. An attractive feature of PAM is this low bandwidth requirementresulting in a

minimal carrier frequency, which would minimize the power dissipation in aswitching power

amplification stage. Unfortunately, PAM is limited by the requirementsfor pulse amplitude

accuracy. It turns out to be problematic to realize a high efficiencypower output stage that can

synthesize the pulses with accurately defined amplitude. If onlya few discrete amplitude levels

are required, as it is the case with the other three pulsemodulat

amplification of the pulses is much simpler.

1 Fundamental pulse modulation methods

1 illustrates these four fundamental principles of analog


modulated pulses as illustrated in Fig. 4.1. The bandwidth requirementsare



attractive feature of PAM is this low bandwidth requirementresulting in a



curacy. It turns out to be problematic to realize a high efficiencypower output stage that can


are required, as it is the case with the other three pulsemodulation methods, the task of power

amplification of the pulses is much simpler.

1 illustrates these four fundamental principles of analog


1. The bandwidth requirementsare



attractive feature of PAM is this low bandwidth requirementresulting in a



curacy. It turns out to be problematic to realize a high efficiencypower output stage that can


ion methods, the task of power

Pulse Width Modulation (PWM) is dramatically different form PAM in that it performssampling

in time whereas PAM provides sampling in amplitude. Consequently, theinformation is cod

into the pulse time position within each switching interval. PWMonly requires synthesis of a few

discrete output levels, which is easily realized bytopologically simple high efficiency switching

power stages. On the other hand, thebandwidth requirements

order of magnitude higher thanPAM. This penalty is well paid given the simplifications in the

switching power stage /power supply.

Pulse Position Modulation (PPM) differs from PWM in that the value of eachinstantaneous

sample of a modulating wave is caused to vary the position in

modulated time of occurrence. Each pulse has identical shapeindependent of the modulation

depth. This is an attractive feature, since a uniform pulse is

Table 4.1 Qualitative comparison of basic pulse modulation methods

simple to reproduce with a simple switching power stage. On the other hand, a limitation ofPPM

is the requirements for pulse amplitude level if reasonable powers are required. Thepower su

level of the switching power stage will have to be much higher than therequired load voltage.

This leads to sub-optimal performance on several parameters asefficiency, complexity and audio

performance.


whereas PAM provides sampling in amplitude. Consequently, theinformation is cod



power stages. On the other hand, thebandwidth requirements for PWM are typically close to an


switching power stage /power supply.


ample of a modulating wave is caused to vary the position in time of apulse, relative to its non


depth. This is an attractive feature, since a uniform pulse is

1 Qualitative comparison of basic pulse modulation methods


is the requirements for pulse amplitude level if reasonable powers are required. Thepower su


optimal performance on several parameters asefficiency, complexity and audio


whereas PAM provides sampling in amplitude. Consequently, theinformation is coded



for PWM are typically close to an



of apulse, relative to its non-



is the requirements for pulse amplitude level if reasonable powers are required. Thepower supply


optimal performance on several parameters asefficiency, complexity and audio

Pulse Density Modulation is based on a unity pul

ofoccurrence for the pulses within the switching period. The modulated parameter is the

of the pulse. For each sample interval it is determined if the pulse should bepresent or not, hence

the designation density modulation. It is appealing to have a unitypulse since this is easier to

realize by a switching power stage. Another advantage is thesimplicity of modulator

implementation. However, PDM requires excess bandwidthgenerally beyond what is required by

e.g. PWM.

A qualitative comparison of the four fundamental methods is shown in Table

PWM are considered relevant, i.e. potential candidates to reach the targetobjectives.

4.4 Pulse-Amplitude Modulation (PAM)

The simplest and most basic form

regularly spaced pulses are varied in proportion to the corresponding sample values of a

continuous message signal; the pulses can be of a rectangular form or some other appropriate

shape.

Dashed curve depicts the waveform of the message signal

modulated rectangular pulses represent the corresponding PAM signal,

Pulse Density Modulation is based on a unity pulse width, height and a constant time

ofoccurrence for the pulses within the switching period. The modulated parameter is the


modulation. It is appealing to have a unitypulse since this is easier to



A qualitative comparison of the four fundamental methods is shown in Table 4.1. OnlyPDM and


Amplitude Modulation (PAM)

The simplest and most basic form of analog pulse modulation.In PAM, the amplitudes of



ve depicts the waveform of the message signal m(t) and the sequence of amplitude

modulated rectangular pulses represent the corresponding PAM signal, s(t).

se width, height and a constant time

ofoccurrence for the pulses within the switching period. The modulated parameter is thepresence


modulation. It is appealing to have a unitypulse since this is easier to



1. OnlyPDM and


In PAM, the amplitudes of



and the sequence of amplitude-

PAM Generation

1. Instantaneous sampling of the message signal m(t) every T

fs = 1/T

s is chosen in accordance with the sampling theorem.

4.Lengthening the duration of each sample so obtained to some constant value T.

Note: In digital circuit technology, these two operations are jointly called

Recovering the message signal from the PAM signal

Assumption: The message signal is limited to bandwidth B and the sampling rate f

the Nyquist rate.

By using flat-top samples to generate a PAM signal, amplitude distortion is introduced.

Aperture effect – the distortion caused by the use of PAM to transmit an analog

bearing signal

4.5 Analog Pulse Density Modulation (PDM)

Pulse density modulation is now investigated more closely. A simple way to realize a PDMbased

amplifier is the use of a conventional analog pulse density modulator with a linearloop filter,

followed by a switching power stage [Kl92]. However, by integrating aswitching a

stage in the noise shaping loop an interesting power PDM topologyarrives as shown in Fig.

This power PDM was first introduced as a method forswitching amplifiers in [Kl92] followed by

subsequent investigations in [Kl93] andrecently in [Iw96]. Unfortunately, there are several

inherent complications with PDM forpulse modulated power amplifier sy

has to be of higher order forsatisfactory performance within the target frequency band, due to the

PAM Generation

of the message signal m(t) every Ts seconds, where the sa

is chosen in accordance with the sampling theorem.

the duration of each sample so obtained to some constant value T.

In digital circuit technology, these two operations are jointly called “sample and hold.”

Recovering the message signal from the PAM signal

The message signal is limited to bandwidth B and the sampling rate f

top samples to generate a PAM signal, amplitude distortion is introduced.

the distortion caused by the use of PAM to transmit an analog

Analog Pulse Density Modulation (PDM)

modulation is now investigated more closely. A simple way to realize a PDMbased


followed by a switching power stage [Kl92]. However, by integrating aswitching a

stage in the noise shaping loop an interesting power PDM topologyarrives as shown in Fig.



inherent complications with PDM forpulse modulated power amplifier systems. The loop filter


seconds, where the sampling rate

the duration of each sample so obtained to some constant value T.

“sample and hold.”

The message signal is limited to bandwidth B and the sampling rate fs is larger than

top samples to generate a PAM signal, amplitude distortion is introduced.

the distortion caused by the use of PAM to transmit an analog-information

modulation is now investigated more closely. A simple way to realize a PDMbased


followed by a switching power stage [Kl92]. However, by integrating aswitching amplification

stage in the noise shaping loop an interesting power PDM topologyarrives as shown in Fig. 4.4.



stems. The loop filter


immense amount ofnoise generated by the pulse modulating quantizer. The realization of higher

order loopfilters for both analog and di

attention inprevious research. An attractive higher order topology was presented in [Ch90], and

isshown in Fig. 4.3. This higher order structure is suited for analog power PDM systems as

Fig. 4.3 Higher order analog PDM loop filter realization.


order loopfilters for both analog and digital pulse density modulators have received much


3. This higher order structure is suited for analog power PDM systems as

Fig. 4.2 Power SDM topology.

3 Higher order analog PDM loop filter realization.


gital pulse density modulators have received much


3. This higher order structure is suited for analog power PDM systems as

shown in [kl93]. Unfortunately, there are limits on filter order when implemented in theanalog

domain due to tolerances and other analog imperfections. A fourth (or higher) orderfilter is

generally necessary for optimal implementation of power PDM system inreasonable quality.

Even with a fourth order filter, the resulting sampling frequency is inthe range 4.5MHz - 3MHz

for reasonable audio performance in the general case where thetarget bandwidth is 20KHz.

Subsequently, the pulse repetition frequency will be 50-100times the bandwidth limit of a full

audio range system [Kl92]. This is problematic sincephysical limitations within the switching

power amplification stage will introduceswitching losses and error that increase with switching

frequency. Especially the quiescent

power dissipation will be compromised by a high switching frequency. A further drawbackis the

limits on modulation depth with a higher order PDM [Kl92, Kl93]. This will furthercompromise

efficiency and quiescent power dissipation since the pulse amplitude levelswill get relatively

higher. In conclusion, the simple and elegant analog power PDMtopology is compromised by

several essential limitations, mostly relating to the poweramplification stage. Consequently,

analog PDM is not considered optimal for PMAimplementation since PWM as it will become

apparent does not suffer from suchdrawbacks to the same degree.

4.6 Analog Pulse Width Modulation

In general, previous research in the field of pulse width modulation as e.g. [Bl53],

[Ma67],[Bo75a], [Bo75b], [Se87], [Me91], [Go92], [Hi94] has focused on a limited set

ofschemes. No coherent work exists with a comprehensive analysis and comparison of

pulsewidth modulation methods, and certainly not with PMAs as a specific application.

Furthermotivating factors for a detailed review and comparison of PWM methods schemes is

thatinteresting characteristics of the more known modulation schemes have not drawnsufficient

attention. Traditionally, pulse width modulation is categorized in two majorclasses by the

sampling method: natural sampled PWM (NPWM) and uniform sampledPWM (UPWM).

Alternative sampling methods exists which can be categorized as hybridsampling methods since

the nature of sampling lies between the natural and uniformsampling. The principles of the

different sampling methods are illustrated in Fig. 4.4. Thissection focuses on inherently analog

pulse modulation methods. The “digital” UPWM andhybrid sampled PWM are discussed in the

next chapter. Besides the sampling method,PWM is traditionally also differentiated by the edge

modulation and by the class. The edgemodulation may be single sided or double sided. The

modulation of both edges doubles theinformation stored in the resulting pulse train, although the

pulse train frequency is thesame. Class AD and Class BD are the (somewhat misleading but

standardized)

Fig.

Fig. 4.4 Samplings methods in PWM.

abbreviations to differentiate between two

in[Ma70]. Although the approach of synthesizing three

themethod in [Ma70], the designation BD is kept during this fundamental analysis forcoherence

with previous work. The resulting four fundamental NPWM schemes aresummarized in Table

4.4. An abbreviation has been assigned for each scheme i

the methods:

Sampling MethodSwitchingEdge

An example is NADS for Natural sampling

Allmethods can be realized by 4 independently controlled switches using the bridge

switchingpower stage topology shown in Fig.

timedomain waveforms for the considered 4 variants of

to bottom the modulating signal and carrier, the signal waveforms on each of the bridgephases

and the differential- and common

investigation is clear that significantly different modulation schemes in terms ofboth differential

and common mode output, can be synthesized with the simple 4

Table 4.2 Fundamental pulse width modulation schemes

abbreviations to differentiate between two-level and three-level switching as introduced

in[Ma70]. Although the approach of synthesizing three-level waveforms here differs from



An abbreviation has been assigned for each scheme in order toable to differentiate between

Sampling MethodSwitchingEdge

atural sampling - AD switching - Single sided modulation.


switchingpower stage topology shown in Fig. 4.5. Fig. 4.6 - Fig. 4.9 illustrates the essential

timedomain waveforms for the considered 4 variants of NPWM. The figures illustrates fromtop


and common-mode output signals, respectively. From this timedomain

cantly different modulation schemes in terms ofboth differential

and common mode output, can be synthesized with the simple 4-switch Hbridgetopology.

2 Fundamental pulse width modulation schemes

level switching as introduced

here differs from



n order toable to differentiate between

ingle sided modulation.


9 illustrates the essential

NPWM. The figures illustrates fromtop


mode output signals, respectively. From this timedomain

cantly different modulation schemes in terms ofboth differential

switch Hbridgetopology.

Fig.

4.7 Pulse-position modulation (PPM)

In this the position of a pulse relative to its unmodulated time of occurrence is varied in

accordance with the message signal. Pulse

modulation in which M message bits are encoded by transmitting a single pulse in one of 2M

possible time-shifts. This is repeated every T seconds, such that the transmitted bit rate is M/T

bits per second. It is primarily useful for

be little or no multipath interference.

Fig. 4.5 H-bridge switching topology

position modulation (PPM)


accordance with the message signal. Pulse-position modulation (PPM) is a form of signal

in which M message bits are encoded by transmitting a single pulse in one of 2M

shifts. This is repeated every T seconds, such that the transmitted bit rate is M/T

bits per second. It is primarily useful for optical communications systems, where there tends to

interference.


position modulation (PPM) is a form of signal

in which M message bits are encoded by transmitting a single pulse in one of 2M

shifts. This is repeated every T seconds, such that the transmitted bit rate is M/T

systems, where there tends to

4.8 Signal-To-Noise Ratios In Pulse Systems

Intuitively, the PCM transmission bandwidth must be about 2m greater than the signal

bandwidth in order to transmit the PCM bits width minimum distortion. Noise increases with the

square root of the bandwidth so that the PCM signal to noise ratio (SNR) would be less than the

direct transmission SNR by a factor of v(2m). However, the PCM signal is composed only of

binary pulses and the receiver need only decide if a “one” or a “zero” was transmitted. The SNR

needed for a reliable decision is relatively small, typically about 4:1 is sufficient. If 8 bit

quantization were used, a direct transmission channel SNR of greater than 100:1 would be

required to maintain the 8 bit signal precision. Using PCM, a band width increase of about 16:1

would be required, increasing the transmission noise by about 4:1, however , a channel SNR of

only 4:1 or 5:1 would be required. Thus, the PCM transmission would require about a 20:1 SNR

defined in a bandwidth equal to the signal bandwidth for the PCM system compared to over

100:1 SNR for direct transmission. Thus PCM has exchanged bandwidth for signal to noise ratio.

In 1959, C.E. Shannon published a key development in communications theory in which he

propsed a theoretical bound for communication over a noisy analog channel. Shannon developed

the channel capacity bound:

C=W log 2 (1+ SNR )

Where C= the channel capacity in bits per second, W= the channel bandwidth in Herts, and SNR

= the channel signal to noise ratio.

Shannon’s bound is very interesting because it asserts that there exist coding schemes

which will allow the channel capacity to be reached with arbitrarily small error rate. Further

theorem suggests that capacity can be traded for signal to noise ratio.

4.9 Summary

A comprehensive investigation of analog pulse modulation methods has been carried

outwith the primary motivation to devise optimal modulation strategies for PMA systems.This

has involved a fundamental analysis and comparison of known methods followed

byinvestigations of new enhanced pulse modulation methods with improved characteristics.An

initial investigation of PAM, PPM, PWM and PDM concluded on the advantages ofPWM.

Following, the tonal behavior of the four fundamental NPWM schemes wasanalyzed by

developing DFS expressions for the differential and common modecomponents of the modulated

output.

4.10 Keywords

PAM

PPM

PWM

PDM

4.11 Exercise

1. Explain Analog Pulse Density Modulation (PDM).

2. Explain Analog Pulse Width Modulation.

3. Define PPM.

.

Unit 1

DM and PCM

Structure

1.1 Introduction

1.2 Objectives

1.3 Delta modulation and DPCM

1.4 Pulse-Code Modulation

1.5 Comparison of PCM and DM

1.6 Summary

1.7 Keywords

1.8 Exercise

1.1 Introduction

In electronics, modulation is the process of varying one or more properties of a high-

frequency periodic waveform, called the carrier signal, with a modulating signal which typically

contains information to be transmitted. This is done in a similar fashion to

a musician modulating a tone (a periodic waveform) from a musical instrument by varying

its volume, timing and pitch. The three key parameters of a periodic waveform are

its amplitude ("volume"), its phase ("timing") and its frequency ("pitch"). Any of these properties

can be modified in accordance with a low frequency signal to obtain the modulated signal.

Typically a high-frequencysinusoid waveform is used as carrier signal, but a square wave pulse

train may also be used.

In telecommunications, modulation is the process of conveying a message signal, for

example a digital bit stream or an analog audio signal, inside another signal that can be

physically transmitted. Modulation of a sine waveform is used to transform a baseband message

signal into a pass band signal, for example low-frequency audio signal into a radio-frequency

signal (RF signal). In radio communications, cable TV systems or the public switched telephone

network for instance, electrical signals can only be transferred over a limited pass band

frequency spectrum, with specific (non-zero) lower and upper cutoff frequencies. Modulating a

sine-wave carrier makes it possible to keep the frequency content of the transferred signal as

close as possible to the centre frequency (typically the carrier frequency) of the pass band.

1.2 Objectives


• Explain Delta modulation and DPCM.

• Define PCM.

• Give the Comparison of PCM and DM.

1.3 Delta modulation and DPCM

PCM is powerful, but quite complex coders and decoders are

resolution also requires a higher number of bits per sample.

memory—each sample value is separately

which overcomes some limitations of

One way of doing this is to perform source coding using

The signal is first quantized into discrete levels, but the size of the step between

is kept constant. The signal may therefore only make a

one. Once the quantization operation is

sending a zero for a negative transition, and a one for a positive transition. Note that thi


For the above case, the transmitted bit train would be 111100010111110.

Delta modulation and DPCM

PCM is powerful, but quite complex coders and decoders are required. An increase in

resolution also requires a higher number of bits per sample. Standard PCM systems have no

each sample value is separately encoded into a series of binary digits. An alternative,

limitations of PCM, is to use past information in the encoding process.

way of doing this is to perform source coding using delta modulation:

into discrete levels, but the size of the step between adjacent samples

may therefore only make a transition from one level to an adjacent

operation is performed, transmission of the signal can be achieved by

negative transition, and a one for a positive transition. Note that thi

change at each sampling point.

For the above case, the transmitted bit train would be 111100010111110.

required. An increase in

Standard PCM systems have no

encoded into a series of binary digits. An alternative,

use past information in the encoding process.

adjacent samples

transition from one level to an adjacent

performed, transmission of the signal can be achieved by

negative transition, and a one for a positive transition. Note that this means

The demodulator for a delta-modulated signal is simply a staircase generator.

received, the staircase increments positively, and if a zero is

followed by a low pass filter. The key to using delta modulation is to make the right choice of

step size and sampling period —

for the steps to follow, a situation called

step size and the sampling period

If the signal has a known upper


For a DM system with step size a

we require

modulated signal is simply a staircase generator.

increments positively, and if a zero is received, negatively. This is usually

The key to using delta modulation is to make the right choice of

—an incorrect selection will mean that the signal c

for the steps to follow, a situation called overloading. Important parameters are therefore the

sampling period.

If the signal has a known upper-frequency cutoff ωm, then we can estimate the

can change. Assuming that the signal is f(t)=b cos(ωmt), the maximum slope is given by

a, the maximum rate of rise that can be handled is

modulated signal is simply a staircase generator. If a one is

received, negatively. This is usually

The key to using delta modulation is to make the right choice of

an incorrect selection will mean that the signal changes too fast

parameters are therefore the

, then we can estimate the fastest rate at

, the maximum slope is given by

handled is a/T= a fs , so

Making the assumption that the quantisation noise in

mean-square quantisation error power is

all frequencies up to the sampling frequency

DM receiver —if the cutoff frequency is set to the maximum frequency

power in the reconstructed signal is


when the slope overload condition is just met. The SNR therefore increases by 9dB for every

doubling of the sampling frequency.

Delta modulation is extremely simple, and gives

but is clearly limited. One way of attempting to improve

where the step size is not required to be

space shuttles make use of this te

size is encoded as a (multiple bit) PCM signal, and transmitted to the receiver

Differential PCM is similar, but encodes the difference between

—this can further reduce the number of bits

Making the assumption that the quantisation noise in DM is uniformly distributed over(

square quantisation error power is a2/3. We assume that this power is spread evenly over

sampling frequency fs . However, there is still the low pass

the cutoff frequency is set to the maximum frequency fm, then

power in the reconstructed signal is


the slope overload condition is just met. The SNR therefore increases by 9dB for every

doubling of the sampling frequency.

Delta modulation is extremely simple, and gives acceptable performance in many applications,

but is clearly limited. One way of attempting to improve performance is to use

where the step size is not required to be constant. (The voice communication systems on the US

use of this technique.) Another is to use delta PCM, where each desired step

size is encoded as a (multiple bit) PCM signal, and transmitted to the receiver

Differential PCM is similar, but encodes the difference between a sample and its

this can further reduce the number of bits required for transmission.

distributed over(-a, a), the

We assume that this power is spread evenly over

low pass filter in the

, then the total noise

the slope overload condition is just met. The SNR therefore increases by 9dB for every

performance in many applications,

performance is to use adaptive DM,

constant. (The voice communication systems on the US

chnique.) Another is to use delta PCM, where each desired step

size is encoded as a (multiple bit) PCM signal, and transmitted to the receiver as a codeword.

a sample and its predicted value

2.4 Pulse-Code Modulation

PULSE-CODE MODULATION (PCM) refers to a system in which the standard values

of a QUANTIZED WAVE (explained in the following paragraphs) are indicated by a series of

coded pulses. When these pulses are decoded, they indicate the standard values of the original

quantized wave. These codes may be binary, in which the symbol for each quantized element

will consist of pulses and spaces: ternary, where the code for each element consists of any one of

three distinct kinds of values (such as positive pulses, negative pulses, and spaces); or n-ary, in

which the code for each element consists of nay number (n) of distinct values. This discussion

will be based on the binary PCM system. All of the pulse-modulation systems discussed

previously provides methods of converting analog wave shapes to digital wave shapes (pulses

occurring at discrete intervals, some characteristic of which is varied as a continuous function of

the analog wave). The entire range of amplitude (frequency or phase) values of the analog wave

can be arbitrarily divided into a series of standard values. Each pulse of a pulse train [figure 2-

48, view (B)] takes the standard value nearest its actual value when modulated. The modulating

wave can be faithfully reproduced, as shown in views (C) and (D). The amplitude range has been

divided into 5 standard values in view (C). Each pulse is given whatever standard value is

nearest its actual instantaneous value. In view (D), the same amplitude range has been divided

into 10 standard levels. The curve of view (D) is a much closer approximation of the modulating

wave, view (A), than is the 5-level quantized curve in view (C). From this you should see that

the greater the number of standard levels used, the more closely the quantized wave

approximates the original. This is also made evident by the fact that an infinite number of

standard levels exactly duplicate the conditions of non-quantization (the original analog

waveform).

Figure 1.4a. - Quantization levels. MODULATION

Figure 1.4b. - Quantization levels. TIMING

Figure 1.4c. - Quantization levels. QUANTIZED 5-LEVEL

Figure 1.4d. - Quantization levels. QUANTIZED 10-LEVEL

Although the quantization curves of figure 1.4 are based on 5- and 10-level quantization, in

actual practice the levels are usually established at some exponential value of 2, such as 4(22),

8(23), 16(2

4), 32(2

5) . . . N(2

n). The reason for selecting levels at exponential values of 2 will

become evident in the discussion of PCM. Quantized fm is similar in every way to quantized

AM. That is, the range of frequency deviation is divided into a finite number of standard values

of deviation. Each sampling pulse results in a deviation equal to the standard value nearest the

actual deviation at the sampling instant. Similarly, for phase modulation, quantization establishes

a set of standard values. Quantization is used mostly in amplitude- and frequency-modulated

pulse systems.

Figure 1.4e shows the relationship between decimal numbers, binary numbers, and a pulse-code

waveform that represents the numbers. The table is for a 16-level code; that is, 16 standard

values of a quantized wave could be represented by these pulse groups. Only the presence or

absence of the pulses are important. The next step up would be a 32-level code, with each

decimal number represented by a series of five binary digits, rather than the four digits of figure

2-49. Six-digit groups would provide a 64-level code, seven digits a 128-level code, and so forth.

Figure 2-50 shows the application of pulse-coded groups to the standard values of a quantized

wave.

Figure 1.4e. - Binary numbers and pulse-code equivalents.

Figure 1.4 f. - Pulse-code modulation of a quantized wave (128 bits).

In figure 1.4f the solid curve represents the unquantized values of a modulating sinusoid. The

dashed curve is reconstructed from the quantized values taken at the sampling interval and shows

a very close agreement with the original curve. Figure 1.4gis identical to figure 1.4f except that

the sampling interval is four times as great and the reconstructed curve is not faithful to the

original. As previously stated, the sampling rate of a pulsed system must be at least twice the

highest modulating frequency to get a usable reconstructed modulation curve. At the sampling

rate of figure 1.4f and with a 4-element binary code, 128 bits (presence or absence of pulses)

must be transmitted for each cycle of the modulating frequency. At the sampling rate of figure 2-

51, only 32 bits are required; at the minimum sampling rate, only 8 bits are required.

Figure 1.4g. - Pulse-code modulation of a quantized wave (32 bits).

As a matter of convenience, especially to simplify the demodulation of PCM, the pulse trains

actually transmitted are reversed from those shown in figures 1.4e, 1.4f, and 1.4g; that is, the

pulse with the lowest binary value (least significant digit) is transmitted first and the succeeding

pulses have increasing binary values up to the code limit (most significant digit). Pulse coding

can be performed in a number of ways using conventional circuitry or by means of special

cathode ray coding tubes. One form of coding circuit is shown in figure 1.4h. In this case, the

pulse samples are applied to a holding circuit (a capacitor which stores pulse amplitude

information) and the modulator converts PAM to PDM. The PDM pulses are then used to gate

the output of a precision pulse generator that controls the number of pulses applied to a binary

counter. The duration of the gate pulse is not necessarily an integral number of the repetition

pulses from the precisely timed clock-pulse generator. Therefore, the clock pulses gated into the

binary counter by the PDM pulse may be a number of pulses plus the leading edge of an

additional pulse. This "partial" pulse may have sufficient duration to trigger the counter, or it

may not. The counter thus responds only to integral numbers, effectively quantizing the signal

while, at the same time, encoding it. Each bistable stage of the counter stores ZERO or a ONE

for each binary digit it represents (binary 1110 or decimal 14 is shown in figure 1.4h). An

electronic commutator samples the 20, 2

1, 2

2, and 2

3digit positions in sequence and transmits a

mark or space bit (pulse or no pulse) in accordance with the state of each counter stage. The

holding circuit is always discharged and reset to zero before initiation of the sequence for the

next pulse sample.

Figure 1.4h. - Block diagram of quantizer and PCM coder.

The PCM demodulator will reproduce the correct standard amplitude represented by the pulse-

code group. However, it will reproduce the correct standard only if it is able to recognize

correctly the presence or absence of pulses in each position. For this reason, noise introduces no

error at all if the signal-to-noise ratio is such that the largest peaks of noise are not mistaken for

pulses. When the noise is random (circuit and tube noise), the probability of the appearance of a

noise peak comparable in amplitude to the pulses can be determined. This probability can be

determined mathematically for any ration of signal-to-average-noise power. When this is done

for 105 pulses per second, the approximate error rate for three values of signal power to average

noise power is:

17 dB - 10 errors per second

20 dB - 1 error every 20 minutes

22 dB - 1 error every 2,000 hours

Above a threshold of signal-to-noise ration of approximately 20 dB, virtually no errors occur. In

all other systems of modulation, even with signal-to-noise ratios as high as 60 dB, the noise will

have some effect. Moreover, the PCM signal can be retransmitted, as in a multiple relay link

system, as many times as desired, without the introduction of additional noise effects; that is,

noise is not cumulative at relay stations as it is with other modulation systems.

The system does, of course, have some distortion introduced by quantizing the signal. Both the

standard values selected and the sampling interval tends to make the reconstructed wave depart

from the original. This distortion, called QUANTIZING NOISE, is initially introduced at the

quantizing and coding modulator and remains fixed throughout the transmission and

retransmission processes. Its magnitude can be reduced by making the standard quantizing levels

closer together. The relationship of the quantizing noise to the number of digits in the binary

code is given by the following standard relationship:

Where:

n is the number of digits in the binary code

Thus, with the 4-digit code of figure 2-50 and 2-51, the quantizing noise will be about 35 dB

weaker than the peak signal which the channel will accommodate.

1.5 Comparison of PCM and DM

I. Signal-to-noise ratio of DM is larger than signal-to-noise ratio of PCM.

II. For an ADM signal-to-noise ratio is comparable to Signal-to-noise ratio of

companded PCM.

III. In PCM, that it transmits all the bits which are used to code a sample, whereas in

DM transmits only one bit for one sample.

IV. In PCM system Highest Bandwidth is required since the number of bits are high,

but in DM system lowest bandwidth is only required.

V. PCM system is complex in design when compared to DM system.

VI. No feedback exists in case of PCM system, but feedback exists in DM system.

1.6 Summary

Delta modulation (DM or ∆-modulation)is an analog-to-digital and digital-to-analog

signal conversion technique used for transmission of voice information where quality is not of

primary importance. DM is the simplest form of differential pulse-code modulation (DPCM)

where the difference between successive samples is encoded into n-bit data streams. In delta

modulation, the transmitted data is reduced to a 1-bit data stream. Its main features are:

the analog signal is approximated with a series of segments

each segment of the approximated signal is compared to the original analog wave to

determine the increase or decrease in relative amplitude

the decision process for establishing the state of successive bits is determined by this

comparison

only the change of information is sent, that is, only an increase or decrease of the signal

amplitude from the previous sample is sent whereas a no-change condition causes the

modulated signal to remain at the same 0 or 1 state of the previous sample.

The advantages of PCM are two-fold. First, noise interference is almost completely

eliminated when the pulse signals exceed noise levels by a value of 20 dB or more. Second, the

signal may be received and retransmitted as many times as may be desired without introducing

distortion into the signal.

1.7 Keywords

• DM

• PCM

• DPCM

• Carrier signal,

• Modulating signal

• Sampling period

1.8 Exercise

1) Pulse-code modulation requires the use of approximations of value that are obtained by

what process?

2) If a modulating wave is sampled 10 times per cycle with a 5-element binary code, how

many bits of information are required to transmit the signal?

3) What is the primary advantage of pulse-modulation systems?

4) Give the comparison between PCM and DM.

Unit 2

Pulse Code Modulation-1

Structure

2.1 Introduction

2.2 Objectives

2.3 PCM Reception and Noise

2.4 Uniform Quantization Noise Analysis

2.5 Aperture Time

2.6 Summary

2.7 Keywords

2.8 Exercise

2.1 Introduction

PCM is a term which was formed during the development of digital audio transmission

standards. Digital data can be transported robustly over long distances unlike the analog data and

can be interleaved with other digital data so various combinations of transmission channels can

be used. In the text which follows this term will apply to encoding technique which means

digitalization of analog information in general. In this we go through the Uniform Quantization

Noise Analysis.

2.2 Objectives


• Know PCM Reception And Noise

• Explain Uniform Quantization Noise Analysis

• Define Aperture Time

2.3 PCM Reception And Noise

PCM is a method of converting an analog into digital signals. Information in an analog

form cannot be processed by digital computers so it's necessary to convert them into digital form.

PCM is a term which was formed during the development of digital audio transmission

standards. Digital data can be transported robustly over long distances unlike the analog data and

can be interleaved with other digital data so various combinations of transmission channels can

be used. In the text which follows this term will apply to encoding technique which means

digitalization of analog information in general.

PCM doesn`t mean any specific kind of compression, it only implies PAM (pulse

amplitude modulation) - quantization by amplitude and quantization by time which means

digitalization of the analog signal. The range of values which the signal can achieve

(quantization range) is divided into segments; each segment has a segment representative of the

quantization level which lies in the middle of the segment. To every quantization segment (and

quantization level) one and unique code word (stream of bits) is assigned. The value that a signal

has in certain time is called a sample. The process of taking samples is called quantization by

time. After quantization by time, it is necessary to conduct quantization by amplitude.

Quantization by amplitude means that according to the amplitude of sample one quantization

segment is chosen (every quantization segment contains an interval of amplitudes) and then

record segments code word.

To conclude, PCM encoded signal is nothing more than stream of bits.

The first example of PCM encoding

In this example the signal is quantized in 11 time points using 8 quantization segments. All the

values that fall into a specific segment are approximated with the corresponding quantization

level which lies in the middle of a segment. The levels are encoded using this table:

Level Code word

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111

Table1. Quantization levels with belonging code words

The first chart shows the process of signal quantizing and digitizing. The samples shown are

already quantized - they are approximated with the nearest quantization level. To the right of

each sample is the number of its quantization level. This number is converted into a 3-bit code

word using the above table.

Chart 1. Quantization and digitalization of a signal

The second chart shows the process of signal restoration. The restored signal is formed according

to taken samples. It can be noticed that the restored signal diverges from the input signal. This

divergence is a consequence of quantization noise. It always has the same intensity, independent

from the signal intensity. If the signal intensity drops, the quantization noise will be more

noticeable (the signal-to-noise ratio will drop).

Chart 2. Process of restoring a signal.

PCM encoded signal in binary form:

101 111 110 001 010 100 111 100 011 010 101

Total of 33 bits were used to encode a signal.

2.4 Uniform Quantization Noise Analysis

A more quantitative description of the effect of quantization can be obtained using

random signal analysis applied to the quantization error. If the number of bits in the quantizer is

reasonably high and no clip-ping occurs, the quantization error sequence, although it is

completely determined by the signal amplitudes, nevertheless behaves as if it is a random signal

with the following properties :

(Q.1)The noise samples appear to be6uncorrelated with the signal samples.

(Q.2)Under certain assumpt

high rate quantizers, the noise samples appear to be uncorrelated from sample

i.e., e[n] acts like a white noise sequence.

(Q.3)The amplitudes of

range−∆/2< e [n]≤ ∆/2, resulting

These simplifying assumptions allow a linear analysis that yields accurate results if the signal is

not too coarsely quantized. Under these conditions, it can be shown that if the output levels of

the quantizer are optimized, then the quantizer error will

output (however not the quantizer input, as commonly stated).These results can be easily shown

to hold in the simple case of a uniformly distributed memory

how the result can be extended t

With these assumptions, it is possible to derive the following formula for the signal

quantizing-noise ratio (in dB) of a

uniform quantizer:

Where σx and σe are the rms values of t

respectively. The formula of Equation (

(or the number of quantization levels) gets large. It can be way o

large[12]. Figure 2.1 shows a comparison of(

measured for speech signals. The measurements were done by quantizing 16

and 10 bits. The faint dashed lines are from (

for uniform quantization. There is good agreement between these graphs indicating that (

reasonable estimate of SNR.

(Q.2)Under certain assumptions, notably smooth input probability density functions and

noise samples appear to be uncorrelated from sample

e[n] acts like a white noise sequence.

(Q.3)The amplitudes of noise samples are uniformly distributed across the

2, resulting in average powerσ2

e= ∆2/12.



optimized, then the quantizer error will be uncorrelated with the quantizer


to hold in the simple case of a uniformly distributed memory less input and Bennett has shown

result can be extended to inputs with smooth densities if the bit rate is assumed high.

With these assumptions, it is possible to derive the following formula for the signal

noise ratio (in dB) of a B-bit

are the rms values of the input signal and quantization noise samples,

respectively. The formula of Equation (2.1) is an increasingly good approximation as the bit rate

(or the number of quantization levels) gets large. It can be way off, however, if the bit rate is not

shows a comparison of(2.1) with signal-to-quantization

measured for speech signals. The measurements were done by quantizing 16-bit samples to 8, 9,

and 10 bits. The faint dashed lines are from (2.1) and the dark dashed lines are measured values

for uniform quantization. There is good agreement between these graphs indicating that (

ability density functions and

noise samples appear to be uncorrelated from sample-to-sample,

tributed across the



be uncorrelated with the quantizer


ess input and Bennett has shown

is assumed high.

With these assumptions, it is possible to derive the following formula for the signal-to-

he input signal and quantization noise samples,

) is an increasingly good approximation as the bit rate

, however, if the bit rate is not

quantization-noise ratios

bit samples to 8, 9,

re measured values

for uniform quantization. There is good agreement between these graphs indicating that (2.1) is a

Note that Xm is a fixed parameter of the quantizer, while

signal level increases, the ratio X

close to Xm , many samples are clipped, and the assumptions underlying(

This accounts for the precipitous fall in SNR for

Fig. 2.1Comparison ofµ-law and linear quantization for

dashed lines. Measured uniform quantization SNR

(µ =100)compression — solid lines.

Also, it should be noted that (2.1

increasing B by 1 bit (doubling the number of quantization levels) increases the SNR by 6dB. On

the other hand, it is also important to note that halving

words, cutting the signal level in half is like throwing away one bit (half of the levels) of the

quantizer. Thus, it is exceedingly important to keep input signal levels as high as possible

without clipping.

xed parameter of the quantizer, while σx depends on the input signal level. As

Xm/σx decreases moving to the left in Figure 2.1

, many samples are clipped, and the assumptions underlying(2.1) no longer hold.

This accounts for the precipitous fall in SNR for1 < X m/σx< 8.

law and linear quantization for B = 8, 9, 10: Equation (

dashed lines. Measured uniform quantization SNR — dark dashed lines.

solid lines.

2.1) and Figure 2.1 show that with all other parameters being

by 1 bit (doubling the number of quantization levels) increases the SNR by 6dB. On

the other hand, it is also important to note that halving σx decreases the SNR by 6dB. In other



depends on the input signal level. As

2.1. when σx gets

) no longer hold.

10: Equation (2.1) — light

dark dashed lines.µ-law

with all other parameters being fixed,

by 1 bit (doubling the number of quantization levels) increases the SNR by 6dB. On

by 6dB. In other



2.5 Aperture Time

PCM Sampling

- the function of a sampling circuit in a PCM transmitter is to periodically sample the

continually changing analog input voltage and convert those samples to a series of

constant-amplitude pulses that can be more easily be converted to binary PCM code

- For the ADC to accurately convert a voltage to binary code, the voltage must be

relatively constant so that the ADC can complete the conversion before the voltage level

changes. If not, the ADC would be continually attempting to follow the changes and may

never stabilize on any PCM code.

o Two basic techniques used to perform the sampling function:

natural sampling

flat-top sampling

Natural sampling

– is when the tops of the sample pulses retain their natural shape during the sample interval,

making it difficult for an ADC to convert the sample to a PCM code

Flat-top sampling

- is the most common method used for sampling voice signals in PCM systems, which is

accomplished in a sample-and-hold circuit

- the purpose of a sample-and-hold circuit is to periodically sample the continually

changing analog input voltage and convert those samples to a series of constant-

amplitude PAM voltage levels

aperture error – is when the amplitude of the sampled signal changes during the sample pulse

time

aperture or acquisition time – the time that the FET, Q1, of a sample-and-hold circuit is on

aperture distortion – if the input to the ADC is changing while it is performing the conversion

droop – a gradual discharge across the capacitor of a sample-and-hold circuit during conversion

time caused by the capacitor discharging through its own leakage resistance and the input

impedance of the voltage follower Z2

2.6 Summary

Today and in the future, research will be concentrated on developing new PCM signal

compression methods. These compression methods should have higher compression rates,

probably over 100:1 with unnoticeable loss in signal quality. The basic signal quality is

measured by human perception, so various segments of human perception are being studied in

detail. According to these studies compression methods are formed, the signal restored after

compression has only components of the original signal which are above the threshold of

perception. In the 80's compression methods was based on classical information theory. The

basic technique was to find redundancy in data (images, etc.) and according to that to conduct the

compression. Compression of images is segment of data compression which was probably

mostly exploited. So image-compression based on the techniques described above can be called

first generation image coding techniques. The second generation image coding techniques takes

in consideration various aspects of human visual system in order to achieve greater compression

rates without significant loss of image quality. That means that those coding techniques are

lossy, but an important characteristic of this technique is in that it identifies and separate visually

relevant and irrelevant parts of an image and then uses appropriate coding techniques for these

parts.

2.7 Keywords

• PCM

• PAM

• Natural sampling

• Flat-top sampling

• Aperture or acquisition time

2.8 Exercise

1. Explain PCM Reception And Noise.

2. Explain Uniform Quantization Noise Analysis.

3. Define Aperture Time.

Unit 3


Structure

3.1 Introduction

3.2 Objectives

3.3 The S N Ratio And Channel Capacity Of PCM

3.4 Comparison Of PCM With Other Systems

3.5 Pulse rate

3.6 Advantages and applications of Pulse Code Modulation

3.7 Disadvantages of Pulse Code Modulation

3.8 Summary

3.10 Exercise

3.9 Keywords

3.1 Introduction

PCM uses binary numbers to represent each position of the servo. Binary numbers are

integers or whole numbers. There is a finite or limited amount of numbers available to represent

the servo position based on how many bits the system has available. The amount of numbers

available will be 2 to the power of #bits. If it is a 10-bit system there will be 2^10=1024 numbers

available.

Let’s just say we have a 10-bit system with 1024 servo positions. This is digital because there are

only 1024 different positions that the servo can be positioned, with nothing in between those

numbers. In contrast, a PPM system has an infinite amount of positions available which makes it

is analogue.

3.2 Objectives


• Give the S N Ratio And Channel Capacity Of PCM

• Give the Comparison Of PCM With Other Systems

• Define Pulse rate

• List the Advantages and applications of Pulse Code Modulation

• List Disadvantages of Pulse Code Modulation

3.3 The S N Ratio and Channel Capacity of PCM

How fast can we transmit information over a communication channel?

Suppose a source sends r messages per second, and the entropy of a message is H bits per

message. The information rate is R D r H bits/second.

One can intuitively reason that, for a given communication system, as the information rate

increases the number of errors per second will also increase. Surprisingly, however, this is not

the case.

Shannon’s theorem:

• A given communication system has a maximum rate of information C known as the

channel capacity.

• If the information rate R is less than C, then one can approach arbitrarily smal

probabilities by using intelligent coding techniques.

• To get lower error probabilities, the encoder has to work on longer blocks of signal data.

This entails longer delays and higher computational requirements.

Thus, if R <= C then transmission ma

Unfortunately, Shannon’s theorem is not a constructive proof

coding method exists. The proof can therefore not be used to develop a coding method that

reaches the channel capacity.

The negation of this theorem is also true: if R > C, then errors cannot be avoided regardless of

the coding technique used.

1 Shannon-Hartley theorem

Consider a band limited Gaussian channel operating in the presence of additive Gaussian

The Shannon-Hartley theorem states that the channel capacity is given by

A given communication system has a maximum rate of information C known as the

If the information rate R is less than C, then one can approach arbitrarily smal

probabilities by using intelligent coding techniques.

To get lower error probabilities, the encoder has to work on longer blocks of signal data.

This entails longer delays and higher computational requirements.

Thus, if R <= C then transmission may be accomplished without error in the presence of noise.

Unfortunately, Shannon’s theorem is not a constructive proof — it merely states that such a



Consider a band limited Gaussian channel operating in the presence of additive Gaussian

Hartley theorem states that the channel capacity is given by

A given communication system has a maximum rate of information C known as the

If the information rate R is less than C, then one can approach arbitrarily small error

To get lower error probabilities, the encoder has to work on longer blocks of signal data.

y be accomplished without error in the presence of noise.

it merely states that such a



Consider a band limited Gaussian channel operating in the presence of additive Gaussian noise:

where C is the capacity in bits per second, B is the bandwidth of the channel in Hertz, and S=N is

the signal-to-noise ratio.

We cannot prove the theorem, but can partial

Suppose the received signal is accompanied by noise with a RMS voltage of σ , and that the

signal has been quantised with levels separated by

may expect to be able to recognize

Suppose further that each message is to be represented by one voltage level. If there

possible messages, then there must be M levels. The average

The number of levels for a given average signal power is therefore

where N = σ2 is the noise power. If each message is equally likely, then each carries an equal

amount of information


We cannot prove the theorem, but can partially justify it as follows:

uppose the received signal is accompanied by noise with a RMS voltage of σ , and that the

signal has been quantised with levels separated by a= λσ . If λ is chosen sufficiently

recognize the signal level with an acceptable probability of error.

further that each message is to be represented by one voltage level. If there

possible messages, then there must be M levels. The average signal power is then

vels for a given average signal power is therefore

is the noise power. If each message is equally likely, then each carries an equal


uppose the received signal is accompanied by noise with a RMS voltage of σ , and that the

sufficiently large, we

probability of error.

further that each message is to be represented by one voltage level. If there are to be M

signal power is then

is the noise power. If each message is equally likely, then each carries an equal

To find the information rate, we need to estimate how many messages can be carri

time by a signal on the channel. Since the discussion is heuristic, we note that the response of an

ideal LPF of bandwidth B to a unit step has a 10

therefore that with T = 0.5 / B ≈

rate is then

The rate at which information is being transferred across the channel is Therefore

This is equivalent to the Shannon

estimated the rate at which information can be transmitted with reasonably small error

Shannon-Hartley theorem indicates that with

transmission at channel capacity can occur with arbitrarily small error.

The expression of the channel capacity of the Gaussian channel makes intuitive sense:

• As the bandwidth of the channel increases, it is possible to make faster changes in the

information signal, thereby increasing the information rate.

• As S/N increases, one can increase the information rate while still preventing errors due

to noise.

• For no noise, S/N= ∞

bandwidth

Thus we may trade off bandwidth for SNR. For example, if S/N= 7 and B= 4kHz, then the

channel capacity is C = 12* 103

3kHz, the channel capacity remains the same.

nd the information rate, we need to estimate how many messages can be carri


ideal LPF of bandwidth B to a unit step has a 10–90 percent rise time of τ = 0.44/B. We estimate

≈ τ we should be able to reliably estimate the level. The message


This is equivalent to the Shannon-Hartley theorem with λ= 3:5. Note that this discussion has

the rate at which information can be transmitted with reasonably small error

Hartley theorem indicates that with sufficiently advanced coding techniques

transmission at channel capacity can occur with arbitrarily small error.

of the channel capacity of the Gaussian channel makes intuitive sense:

As the bandwidth of the channel increases, it is possible to make faster changes in the

information signal, thereby increasing the information rate.

As S/N increases, one can increase the information rate while still preventing errors due

and an infinite information rate is possible irrespective of


bits/s. If the SNR increases to S=N D 15 and B is decreased to

3kHz, the channel capacity remains the same.

nd the information rate, we need to estimate how many messages can be carried per unit


90 percent rise time of τ = 0.44/B. We estimate

be able to reliably estimate the level. The message


Hartley theorem with λ= 3:5. Note that this discussion has

the rate at which information can be transmitted with reasonably small error — the

advanced coding techniques

of the channel capacity of the Gaussian channel makes intuitive sense:

As the bandwidth of the channel increases, it is possible to make faster changes in the

As S/N increases, one can increase the information rate while still preventing errors due

nite information rate is possible irrespective of


bits/s. If the SNR increases to S=N D 15 and B is decreased to

However, as B =>∞, the channel

bandwidth, the noise power also increases. If the noise power spectral density is

total noise power is N = ηB, so the Shannon

Noting that

and identifying x as x = S/ηB, the channel capacity as B increases without bound becomes

This gives the maximum information transmission rate possible for a system of given power but

no bandwidth limitations.

The power spectral density can be speci

There are literally dozens of coding techniques

and it is an active research subject. Obviously all obey the Shannon

Some general characteristics of the

sending binary digits at a transmission rate equal to the channel capacity: R

, the channel capacity does not become infinite since, with an increase in

bandwidth, the noise power also increases. If the noise power spectral density is

B, so the Shannon-Hartley law becomes

g x as x = S/ηB, the channel capacity as B increases without bound becomes


The power spectral density can be specified in terms of equivalent noise temperature by η=kT

There are literally dozens of coding techniques — entire textbooks are devoted to the subject,

and it is an active research subject. Obviously all obey the Shannon-Hartley theorem.

Some general characteristics of the Gaussian channel can be demonstrated. Suppose we are

sending binary digits at a transmission rate equal to the channel capacity: R = C. If the average

nite since, with an increase in

bandwidth, the noise power also increases. If the noise power spectral density is η /2, then the

g x as x = S/ηB, the channel capacity as B increases without bound becomes


uivalent noise temperature by η=kTeq .

entire textbooks are devoted to the subject,

Hartley theorem.

Gaussian channel can be demonstrated. Suppose we are

C. If the average

signal power is S, then the average energy per bit is Eb

seconds.

With N = ηB, we can therefore write

Rearranging, we find that

This relationship is as follows:

The asymptote is at Eb/η= -1.59dB, so below this value there is no error

any information rate. This is called the Shannon limit.

average energy per bit is Eb = S/C, since the bit duration is 1

With N = ηB, we can therefore write

1.59dB, so below this value there is no error-free communication at

any information rate. This is called the Shannon limit.

C, since the bit duration is 1/C

free communication at

3.4 Comparison of PCM w

The below table shows the comparison

adaptive delta modulation. The comparison is done on the basis of various parameters like

transmission bandwidth, quantization error, number of transmitter bits per sample etc.

Comparison between PCM, adaptive delta modulation and D

modulation.

Next part shows the comparison for voice encoding.

with Other Systems

The below table shows the comparison of PCM, Differential PCM , Delta modulation and



Comparison between PCM, adaptive delta modulation and Differential pulse code

Next part shows the comparison for voice encoding.

Delta modulation and



ifferential pulse code

3.5 Pulse rate

Sampling is obviously a key feature of PCM system. What sampling rate or pulse rate

must be used for a given signal?

must be at least twice the highest frequency of the input signal.

band limited to 4 kilohertz, a minimum sampling rate of 8 kilo samples per second would be

required. This is typical of a voice channel in a telecommunication channel. If the same signal

sample is quantized to 8 bits (28

(8 bits per sample times 8 kilo samples per second).

3.5.1 Bits per Second, Symbols per Second and Bauds

Information rate is normally expressed in “bits per second” where a bit represents a bin

choice, i.e., the information is either a “one” or a “zero

over a communication channel, one, or more, bits are encoded into “symbols” which are

transmitted and the transmission rate is expressed in terms of “sy

“baud” is used interchangeably with symbol rate. It is incorrect it refer to “baud rate” since baud

is defined as a measure of rate. Note that symbol rate is only equal to bit rate when only one bit

is represented by a symbol. It is not uncommon for a transmission symbol to represent several

bits. For example, a 4800 bit per second data modem typically transmits at 1200 baud, or 1200

symbols per second, each symbol representing 4 bits of information.


signal? The sampling theorem answers that question: the sampling rate

must be at least twice the highest frequency of the input signal. If, in our example, the signal is



8 = 128 levels), the PCM bit rate would be 64 kilobits per second

(8 bits per sample times 8 kilo samples per second).

Bits per Second, Symbols per Second and Bauds

Information rate is normally expressed in “bits per second” where a bit represents a bin

, i.e., the information is either a “one” or a “zero”. When binary information is transmitted


transmitted and the transmission rate is expressed in terms of “symbols per second”. The unit



t is not uncommon for a transmission symbol to represent several


symbols per second, each symbol representing 4 bits of information.


t question: the sampling rate

in our example, the signal is



8 levels), the PCM bit rate would be 64 kilobits per second

Information rate is normally expressed in “bits per second” where a bit represents a binary

information is transmitted


mbols per second”. The unit



t is not uncommon for a transmission symbol to represent several


3.6 Advantages and applications of Pulse Code Modulation

The principal advantage of Pulse Code Modulation (PCM) is the noise immunity. But it

is not used exclusively. Other pulse modulation systems are still used in spite of highly superior

performance of PCM. The reasons are that firstly those systems came earlier secondly PCM

needs very complex encoding and quantizing circuitry and thirdly PCM requires larger

bandwidth as compared to analog systems.

In spite of these three implementations PCM is fast gaining popularity and is being used

increasingly. The reasons are very simple. PCM no doubt requires much more complex

modulating procedures than analog systems. But multiplexing equipment is much cheaper.

Further distance between repeaters is large because PCM tolerates much worse signal to noise

ratios. Finally advent of very large scale integration (VLSI) has reduced the cost of complex

circuits needed in PCM. Regarding the increased bandwidth requirements by PCM the problems

is no longer a serious one because of the advent of large band width fiber optic systems. PCM

also finds use in space communications. Way back in 1965 PCM was used by mariners to

transmit back pictures of Mars. Of course each picture took several minutes for transmission.

PCM was obviously the first digital system. However, today several others have come up and are

being used occasionally. Few of them are differential PCM and delta modulation. Differential

modulation is a PCM with the modification that each word in this system indicates the difference

in amplitude, positive or negative, between this sample and the previous one. Thus this system

indicates the relative rather than the absolute value of each sample. In this, therefore, the speech

is redundant, since amplitude is related to the previous one and large variations from one sample

to the next are unlikely. As a result fewer bits are needed to indicate the size of the magnitude

change relative to the case of absolute magnitude. Smaller bandwidth is therefore needed for

transmission. Differential PCM is not popularly used because increased complexity of encoding

and decoding processes outweighs advantages and gained through its use.

Delta modulation is a digital modulation system which in its simplest form may be

equated with the basic form of differential PCM. In a simple delta modulation system just one bit

is sent per sample to indicate whether the signal is larger or smaller than the previous sample.

This system has the merits of having extremely simple coding and decoding procedures. Further

the quantizing process is also very simple. But it has the drawback that it can not easily handle

rapid changes in magnitude and as a result quantizing noise tends to be quite high. Even on using

compounding and modified and complex versions of delta modulation, the transmission race

must be close to hundred kilo bits per second to give the same performance for a telephone

channel as PCM provides with only sixty four kilo bits.

3.7 Disadvantages of Pulse Code Modulation

The advantage of a PCM radio system is that it gives the pilot much finer and more precise

control over the airplane. However, there is a huge drawback. A PCM receiver must translate the

signal from Pulse Code Modulation language to Pulse Position Modulation language before

sending the information to the servos.

If one small byte of information is corrupt, even if it is only for one servo, the translator inside

the receiver gets all confused! The "translator" part of the receiver looks at ALL of the servos

and says “I don’t understand a word the transmitter is saying, so all of you hold your position

until I get the next message!” If only a couple of messages or sequences of information is

corrupt, the pilot will never notice because the servos will stay put at the position of the last

known good signal for a very short period of time (20ms for each bad or corrupt message).

If the signal is corrupt for an extended period of time a PCM receiver will enter “safe mode”.

Safe mode moves all of the servos to a predetermined position. At this point Sir Isaac Newton is

piloting your airplane! Since he’s been dead for a while this is not a good thing!

3.8 Summary

The advantage of a digital signal is that it can be reproduced perfectly. The information is always

decoded as a 0 or 1. There are no gray areas in between to create noise. This means that the

information arriving at the receiver is exactly the same as the information leaving the transmitter.

In contrast, a PPM analogue signal could be distorted by slight interference before it arrives at

the receiver. The Pulse Position Modulation receiver will pass all of the information it gets to the

servos, including interference.

3.9 Keywords

• PCM

• DM

• ADM

• DPCM

3.10 Exercise

1. Give the S N Ratio and Channel capacity of PCM.

2. Give the comparison of PCM with other Systems.

3. Define Pulse rate.

4. List the Advantages and applications of Pulse Code Modulation.

5. List Disadvantages of Pulse Code Modulation.

Unit 4


Structure

4.1 Introduction

4.2 Objectives

4.3 PCM Codescs

4.4 24-Channel PCM

4.5 The PCM Channel Bank

4.6 Multiplex Hierarchy

4.7 Measurements of Quantization Noise

4.8 Differential PCM

4.9 Summary

4.10 Keywords

4.11 Exercise

4.1 Introduction

Meaning of DPCM – “Differential Pulse Code Modulation”, is a modulation technique

invented by the British Alec Reeves in 1937. It is a digital representation of an analog signal

where the magnitude of the signal is sampled regularly at uniform intervals. Every sample is

quantized to a series of symbols in a digital code, which is usually a binary code. PCM is used in

digital telephone systems. It is also the standard form for digital audio in computers and various

compact disc formats. Several PCM streams may be multiplexed into a larger aggregate data

stream. This technique is called Time-Division Multiplexing, or (TDM). TDM was invented by

the telephone industry, but today the technique is an integral part of many digital audio

workstations such as Pro Tools. In conventional PCM, the analog signal may be processed (e.g.

by amplitude compression) before being digitized. Once the signal is digitized, the PCM signal is

not subjected to further processing (e.g. digital data compression). Some forms of PCM combine

signal processing with coding. Older versions of these systems applied the processing in the

analog domain as part of the A/D process; newer implementations do so in the digital domain.

These simple techniques have been largely rendered obsolete by modern transform-based signal

compression techniques.

4.2 Objectives


• Know PCM Codes.

• Explain 24-Channel PCM.

• Explain the PCM Channel Bank.

• Know Multiplex Hierarchy.

• Define DPCM.

4.3 PCM Codecs

Pulse Code Modulation (PCM) codecs are the simplest form of waveform codecs.

Narrowband speech is typically sampled 8000 times per second, and then each speech sample

must be quantized. If linear quantization is used then about 12 bits per sample are needed, giving

a bit rate of about 96 kbits/s. However this can be easily reduced by using non-linear

quantization. For coding speech it was found that with non-linear quantization 8 bits per sample

was sufficient for speech quality which is almost indistinguishable from the original. This gives a

bit rate of 64 kbits/s, and two such non-linear PCM codecs were standardised in the 1960s. In

America u-law coding is the standard, while in Europe the slightly different A-law compression

is used. Because of their simplicity, excellent quality and low delay both these codecs are still

widely used today. For example the .au audio files that are often used to convey sounds over the

Web are in fact just PCM files. For information on how to listen to au and other sound format

files under various operating systems. Code to implement the G711 A-law and u-law codes has

been released into the public domain by Sun Microsystems Inc, and modified by Borge

Lindberg. To FTP this code. For more information about PCM, and other waveform codecs, a

good place to look is the book "Digital Coding of Waveforms" by N.S Jayant and Peter Noll. It

was published by Prentice Hall in 1984, and although its too expensive really to be worth buying,

you might find a copy in your library.

4.4 24-Channel PCM

Time division multiplexing is used at local exchanges to combine a number of

incoming voice signals onto an outgoing trunk. Each incoming channel is allocated a

specific time slot on the outgoing trunk, and has full access to the transmission line

only during its particular time slot. Because the incoming signals are analogue, they

must first be digitized, because TDM can only handle digital signals. Because PCM

samples the incoming signals 8000 times per second, each sample occupies 1/8000

seconds (125 µseconds). PCM is at the heart of the modern telephone system, and

consequently, nearly all time intervals used in the telephone system are multiples of

125 µseconds.

Because of a failure to agree on an international standard for digital transmission, the

systems used in Europe and North America are different. The North American

standard is based on a 24-channel PCM system, wheras the European system is based

on 4.6.2/4.6.4 channels. This system contains 4.6.2 speech channels, a synchronisation

channel and a signalling channel, and the gross line bit rate of the system is 2.048

Mbps (4.6.4 x 64 Kbps). The system can be adapted for common channel signalling,

providing 4.6.3 data channels and employing a single synchronisation channel. The

following details refer to the European system.

The 4.6.2/4.6.4 channel system uses a frame and multiframe structure, with each frame

consisting of 4.6.4 pulse channel time slots numbered 0-4.6.3. Slot 0 contains

the Frame Alignment Word (FAW) and Frame Service Word (FSW). Slots 1-15 and

17-4.6.3 are used for digitised speech (channels 1-15 and 16-4.6.2 respectively). In

each digitised speech channel, the first bit is used to signify the polarity of the sample,

and the remaining bits represent the amplitude of the sample. The duration of each bit

on a PCM system is 488 nanoseconds (ns). Each time slot is therefore 3.904 µseconds

(8 bits x 488 ns). Each frame therefore occupies 125 milliseconds (4.6.4 x 3.904

mseconds).

In order for signalling information (dial pulses) for all 4.6.2 channels to be transmitted,

the multiframe consists of 16 frames numbered 0-15. In frame 0, slot 16 contains the

Multiframe Alignment Word (MFAW) and Multiframe Service Word (MFSW). In

frames 1-15, slot 16 contains signalling information for two channels. The frame and

multiframe structure are shown below. The duration of each multiframe is 2

milliseconds(125 µseconds x 16).

The frame and multiframe structures for a 4.6.2/4.6.4 channel PCM system

4.5 The PCM Channel Bank

To allow the receiver to locate the PCM samples, Bell engineers developing T1 created a

special bit, called the 193rd

bit, and added it between the 24-channel frames. This special bit is

the framing bit. The framing bit creates a repeating pattern of 1s and 0s that a receiver uses to

identify the 193rd

bit. Once the receiver locates the framing bit, it then knows where the PCM

samples for each telephone conversation lie. With the addition of this framing bit, all the

elements of a viable voice digital transmission format are complete.

Twenty-four voice conversations are formatted into a PCM stream that contains an update

PCM samples 8,000 times per second. The 24 PCM samples and the 193rd bit create

format known as DS1 (Digital Signal level 1

constitutes a channel within the DS1 stream. These channels are referred to as

Signal level 0) channels.

The PCM frame codec device has grown to include the capability of creating and

framing bit. This device, which encodes 24 telephone conversations and

framed digital signal is called a channel bank

Figure 4.5.2 shows the completed T1 transmission facility.

the overall bit rate up to 1,544,000 bps.

Figure 4.5.1 : DS1 Format

four voice conversations are formatted into a PCM stream that contains an update

PCM samples 8,000 times per second. The 24 PCM samples and the 193rd bit create

DS1 (Digital Signal level 1). Each PCM sample for a given voice

within the DS1 stream. These channels are referred to as

The PCM frame codec device has grown to include the capability of creating and

framing bit. This device, which encodes 24 telephone conversations and multiplexes them into a

channel bank. It is the channel bank that creates the

shows the completed T1 transmission facility. The addition of the 193rd bit bumps

the overall bit rate up to 1,544,000 bps.

four voice conversations are formatted into a PCM stream that contains an update of the

PCM samples 8,000 times per second. The 24 PCM samples and the 193rd bit create a signal

. Each PCM sample for a given voice signal

within the DS1 stream. These channels are referred to as DS0 (Digital

The PCM frame codec device has grown to include the capability of creating and recovering a

multiplexes them into a

bank that creates the T1 signal.

addition of the 193rd bit bumps

Figure 4.5.2: T1 - A transmission format for DS1

T1 is the ubiquitous digital carrier for telecommunications in North America. T1 was developed

by Bell Laboratories to carry the DS1 signal. It was first tested in Chicago in 1964. T1 was

commercially deployed in New York City in 1962 to improve voice transmission quality and

reduce cabling congestion in underground telephone ducts, where space was at a premium.

The T1 bit rate of 1,544,000 bits per seconds was chosen so the T1 repeaters could be positioned

at about one mile (6000 foot) intervals along a T1 span. This spacing intentionally coincided

with the spacing of voice-frequency load coils, allowing access to both devices at the same

location. Also, 4.544 Mb/s was the upper bit repetition rate for digital transmitters built with the

electronics that were available in the early sixties. Discrete transistors of the day had a top

switching speed of only 6 MHz. T1 is a balanced-circuit transmission system that uses 100 W

characteristic-impedance conductors (typically twisted-pair wire).

4.6 Multiplex Hierarchy

Figure 4.6.1: Voice sampling at 8000 times per Second

The CODEC in Figure 4.6.1

full 125 m seconds between samples to generate the PCM words. In the wasted time gap

PCM samples, PCM samples from other encoded voices can be placed (Figure

time here refers to the ability of the codec to perform A/D and D/A

confused with the sampling rate, which is fixed at 8000 samples per second.

Multiplex Hierarchy

: Voice sampling at 8000 times per Second

4.6.1 is fast enough in its processing that it does not require the

seconds between samples to generate the PCM words. In the wasted time gap

PCM samples, PCM samples from other encoded voices can be placed (Figure 4.6.2

e refers to the ability of the codec to perform A/D and D/A functions. This is not to be

confused with the sampling rate, which is fixed at 8000 samples per second.

is fast enough in its processing that it does not require the

seconds between samples to generate the PCM words. In the wasted time gap between

4.6.2). Processing

functions. This is not to be

Figure

If the PCM coding and decoding process is fast e

into a single stream of PCM words (Figure

transmission line in this manner is called

Figure 4.6.3: Twenty four (24)

Figure 4.6.2: Time Division Multiplexing

If the PCM coding and decoding process is fast enough, many voice conversations can be

into a single stream of PCM words (Figure 4.6.3). Putting many conversations onto a

transmission line in this manner is called Time Division Multiplexing (TDM).

: Twenty four (24) conversations in a PCM Frame

nough, many voice conversations can be stuffed

). Putting many conversations onto a single

conversations in a PCM Frame

Figure 4.6.4: PCM Frame CODEC is

Voice can be encoded by the PCM frame CODEC, but something essential is missing from

digital signal format that allows the CODEC to decode

the digital voice transmission system is not complete yet because the receiver

locating where PCM samples start or end within the

4.7 Measurements of Quantization Noise

Signal-to-noise ratio is defined as the

the background noise (unwanted signal):

where P is average power. Both signal and noise power must be measured at the same or

equivalent points in a system, and within the same system

are measured across the same impedance

square of the amplitude ratio:

: PCM Frame CODEC is almost a complete digital transmission system

Voice can be encoded by the PCM frame CODEC, but something essential is missing from

digital signal format that allows the CODEC to decode received PCM samples. In

the digital voice transmission system is not complete yet because the receiver

locating where PCM samples start or end within the 4.536 Mb/s bit PCM stream.

f Quantization Noise

noise ratio is defined as the power ratio between a signal (meaningful information) and

(unwanted signal):

is average power. Both signal and noise power must be measured at the same or

oints in a system, and within the same system bandwidth. If the signal and the noise

impedance, then the SNR can be obtained by calculating the

a complete digital transmission system

Voice can be encoded by the PCM frame CODEC, but something essential is missing from this

received PCM samples. In Figure 4.6.4,

has no means of

stream.

(meaningful information) and

is average power. Both signal and noise power must be measured at the same or

. If the signal and the noise

, then the SNR can be obtained by calculating the

where A is root mean square (RMS)

signals have a very wide

the logarithmic decibel scale. In deci

which may equivalently be written using amplitude ratios as

The concepts of signal-to

range measures the ratio between the strongest un

discernable signal, which for most purposes

an arbitrary signal level (not necessarily the most powerful signal possible) and noise. Measuring

signal-to-noise ratios requires the selection of a representative or

engineering, the reference signal is usually a

level, such as 1 kHz at +4dBu (4.

SNR is usually taken to indicate an

(near) instantaneous signal-to-noise ratios will be considerably different. The concept can be

understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 's

out'.

4.8 Differential PCM

In PCM, each sample of the waveform is encoded independently of all the other samples.

However, most source signals including speech sampled at the Ny

significant correlation between successive samples. In other words, the average change in

amplitude between successive samples is relatively small. Consequently an encoding scheme that

exploits the redundancy in the samples will res

(RMS) amplitude (for example, RMS voltage). Because many

signals have a very wide dynamic range, SNRs are often expressed using

scale. In decibels, the SNR is defined as

which may equivalently be written using amplitude ratios as

to-noise ratio and dynamic range are closely related. Dynamic

range measures the ratio between the strongest un-distorted signal on a channel and the minimum

discernable signal, which for most purposes is the noise level. SNR measures the ratio between


noise ratios requires the selection of a representative or reference

, the reference signal is usually a sine wave at a standardized nominal

4.228 VRMS).

en to indicate an average signal-to-noise ratio, as it is possible that

noise ratios will be considerably different. The concept can be

understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 's


However, most source signals including speech sampled at the Ny quist rate or faster exhibit



exploits the redundancy in the samples will result in a lower bit rate for the source output.

(for example, RMS voltage). Because many

, SNRs are often expressed using

noise ratio and dynamic range are closely related. Dynamic

and the minimum

is the noise level. SNR measures the ratio between


reference signal. In audio

nominal or alignment

noise ratio, as it is possible that

noise ratios will be considerably different. The concept can be

understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 'stands


rate or faster exhibit



ult in a lower bit rate for the source output.

A relatively simple solution is to encode the differences between successive samples rather than

the samples themselves. The resulting technique is called differential pulse code modulation

(DPCM). Since differences between samples are expected to be smaller than the actual sampled

amplitudes, fewer bits are required to represent the differences. In this case we quantize and

transmit the differenced signal sequence

e(n)= s(n)- s(n - 1),

where s(n) is the sampled sequence of s(t).

A natural refinement of this general approach is to predict the current sample based on

the previous M samples utilizing linear prediction (LP), where LP parameters are dynamically

estimated. Block diagram of a DPCM encoder and decoder is shown below. Part (a) shows

DPCM encoder and part (b) shows DPCM decoder at the receiver.

The "dpcm_demo" shows the use of DPCM to approximate a input sine wave signal and a

speech signal that were sampled at 2 KHz and 44 KHz, respectively. The source code file of the

MATLAB code and the output can be viewed using MATLAB.

To view these you need to download the zipped MATLAB files and sound file into a directory,

unzip them (example: "unzip fname.zip" on unix), then run demo file on MATLAB. To run the

demo file, type "dpcm_demo" at the MATLAB prompt. (Remember the change directory into the

same directory that the files were placed in.)

4.9 Summary

Signal-to-noise ratio (often abbreviated SNR or S/N) is a measure used in science and

engineering to quantify how much a signal has been corrupted by noise. It is defined as the ratio

of signal power to the noise power corrupting the signal. A ratio higher than 1:1 indicates more

signal than noise. While SNR is commonly quoted for electrical signals, it can be applied to any

form of signal. Differential (or Delta) pulse-code modulation encodes the PCM values as

differences between the current and the previous value. For audio this type of encoding reduces

the number of bits required per sample by about 25% compared to PCM. Adaptive DPCM is a

variant of DPCM that varies the size of the quantization step, to allow further reduction of the

required bandwidth for a given signal-to-noise ratio.

4.10 Keywords

• DPCM

• TDM

• PCM

• FSW

• MFSW

• DS0

• DS1

4.11 Exercise

1. Explain PCM Codecs.

2. Explain 24-Channel PCM.

3. Explain the PCM Channel Bank.

4. Explain Multiplex Hierarchy.

5. Define DPCM.

Unit 1

Introduction to Digital Data Transmission

Structure

1.1 Introduction

1.2 Objectives

1.3 Components of a digital communication system

1.4 Summary

1.5 Keywords

1.6 Exercise

1.1 Introduction

Data transmission, digital transmission, or digital communications is the physical

transfer of data (a digital bit stream) over a point-to-point or point-to-multipoint

communication channel. In this chapter we will go through the introduction part of digital data

transmission.

This chapter is concerned with the transmission of information by electrical means using

digital communication techniques. Information may be transmitted from one point to another

using either digital or analog communication systems. In a digital communication system, the

information is processed so that it can be represented by a sequence of discrete messages as

shown in Figure 1–1. The digital source in Figure 1–1 may be the result of sampling and

quantizing an analog source such as speech, or it may represent a naturally digital source such as

an electronic mail file. In either case, each message is one of a finite set containing q messages.

If q = 2, the source is referred to as a binary source, and the two possible digit values are called

bits, a contraction for binary digits. Note also that source outputs, whether discrete or analog, are

inherently random. If they were not, there would be no need for a communication system.

For example, expanding on the case where the digital information results from an analog

source, consider a sensor whose output voltage at any given time instant may assume a

continuum of values. This waveform may be processed by sampling at appropriately spaced time

instants, quantizing these samples, and converting each quantized sample to a binary number

(i.e., an analog-to-digital converter). Each sample value is therefore represented by a sequence of

1s and 0s, and the communication system associates the message 1 with a transmitted signal s1

(t) and the message 0 with a transmitted signal s0 (t). During each signaling interval either the

message 0 or 1 is transmitted with no other possibilities. In practice, the transmitted signals s0 (t)

and s1 (t) may be conveyed by the following means (other representations are possible):

1. By two different amplitudes of a sinusoidal signal, say, A0 and A1

2. By two different phases of a sinusoidal signal, say, ∏/2 and − ∏/2 radians

3. By two different frequencies of a sinusoidal signal, say, f0 and f1 hertz

In an analog communication system, on the other hand, the sensor output would be used directly

to modify some characteristic of the transmitted signal, such as amplitude, phase, or fr

with the chosen parameter varying over a continuum of values.

FIGURE 1–1 Simplified block diagram for a digital communication system

Interestingly, digital transmission of information actually preceded that of analog

transmission, having been used for signaling for military purposes since antiquity through the use

of signal fires, semaphores, and reflected sunlight. The invention of the telegraph, a device for

digital data transmission, preceded the invention of the telephone, an analog communica

instrument, by more than thirty-five years.

Following the invention of the telephone, it appeared that analog transmission would become the

dominant form of electrical communications. Indeed, this was true for almost a century until

today, when digital transmission is replacing even traditionally analog transmission areas.

Several reasons may be given for the move toward digital communications:

1. In the late 1940s it was recognized that regenerative repeaters could be used to reconstruct the

digital signal essentially error free at appropriately spaced intervals. That is, the effects of noise

and channel-induced distortions in a digital communications link can be almost completely

removed, whereas a repeater in an analog system (i.e., an amplifier) re

distortion together with the signal.

2. A second advantage of digital representation of information is the flexibility inherent in the

processing of digital signals. That is, a digital signal can be processed independently of wheth

it represents a discrete data source or a digitized analog source. This means that an essentially

unlimited range of signal conditioning and processing options is available to the designer.


to modify some characteristic of the transmitted signal, such as amplitude, phase, or fr

with the chosen parameter varying over a continuum of values.

1 Simplified block diagram for a digital communication system


ed for signaling for military purposes since antiquity through the use


digital data transmission, preceded the invention of the telephone, an analog communica

five years.



al transmission is replacing even traditionally analog transmission areas.

Several reasons may be given for the move toward digital communications:


signal essentially error free at appropriately spaced intervals. That is, the effects of noise

induced distortions in a digital communications link can be almost completely

removed, whereas a repeater in an analog system (i.e., an amplifier) regenerates the noise and

distortion together with the signal.


processing of digital signals. That is, a digital signal can be processed independently of wheth




to modify some characteristic of the transmitted signal, such as amplitude, phase, or frequency,

1 Simplified block diagram for a digital communication system


ed for signaling for military purposes since antiquity through the use


digital data transmission, preceded the invention of the telephone, an analog communications



al transmission is replacing even traditionally analog transmission areas.


signal essentially error free at appropriately spaced intervals. That is, the effects of noise

induced distortions in a digital communications link can be almost completely

generates the noise and


processing of digital signals. That is, a digital signal can be processed independently of whether



Depending on the origination and intended destination of the information being conveyed, these

might include source coding, compression, encryption, pulse shaping for spectral control,

forward error correction (FEC) coding, special modulation to spread the signal spectrum, and

equalization to compensate for channel distortion. These terms and others will be defined and

discussed throughout the book.

3. The third major reason for the increasing popularity of digital data transmission is that it can

be used to exploit the cost effectiveness of digital integrated circuits. Special-purpose digital

signal-processing functions have been realized as large-scale integrated circuits for several years,

and more and more modem functions are being implemented in ever smaller packages (e.g., the

modem card in a laptop computer). The development of the microcomputer and of special

purpose programmable digital signal processors mean that data transmission systems can now be

implemented as software. This is advantageous in that a particular design is not “frozen” as

hardware but can be altered or replaced with the advent of improved designs or changed

requirements.

4. A fourth reason that digital transmission of information is the format of choice in a majority of

applications nowadays is that information represented digitally can be treated the same

regardless of its origin, as already pointed out, but more importantly easily intermixed in the

process of transmission. An example is the Internet, which initially was used to convey packets

or files of information or relatively short text messages. As its popularity exploded in the early

1990s and as transmission speeds dramatically increased, it was discovered that it could be used

to convey traditionally analog forms of information, such as audio and video, along with the

more traditional forms of packetized information.

In the remainder of this chapter, some of the systems aspects of digital communications are

discussed. The simplified block diagram of a digital communications system shown in Figure 1–

1 indicates that any communications system consists of a transmitter, a channel or transmission

medium, and a receiver.

To illustrate the effect of the channel on the transmitted signal, we return to the binary source

case considered earlier. The two possible messages can be represented by the set 0, 1 where

the 0s and ls are called bits (for binary digit) as mentioned previously. If a 0 or a 1 is emitted

from the source every T seconds, a 1 might be represented by a voltage pulse of A volts T

seconds in duration and a 0 by a voltage pulse o

waveform appears as shown in Figure 1

channel that results in the waveform of Figure 1

some of the noise followed by a sampler. The filtered output is shown in Figure 1

samples are shown in Figure 1–2d. If a sample is greater than 0, it is decided that A was sent; if it

is less than 0 the decision is

FIGURE 1–2 Typical waveforms in a simple dig

filter/sampler/thresholder for a detector: (a) undistorted digital signal; (b) noise plus signal; (c)


seconds in duration and a 0 by a voltage pulse of −A volts T seconds in duration. The transmitted

waveform appears as shown in Figure 1–2a. Assume that noise is added to this waveform by the

channel that results in the waveform of Figure 1–2b. The receiver consists of a filter to remove

e followed by a sampler. The filtered output is shown in Figure 1

2d. If a sample is greater than 0, it is decided that A was sent; if it

2 Typical waveforms in a simple digital communication system that uses a



−A volts T seconds in duration. The transmitted

2a. Assume that noise is added to this waveform by the

2b. The receiver consists of a filter to remove

e followed by a sampler. The filtered output is shown in Figure 1–2c and the

2d. If a sample is greater than 0, it is decided that A was sent; if it

ital communication system that uses a


filtered noisy signal; (d) hard-limited samples of filtered noisy signal—decision = 1 if sample > 0

and −1 if sample < 0. Note the errors resulting from the fairly high noise level.

that a −A was sent. Because of the noise added in the channel, errors may be made in this

decision process. Several are evident in Figure 1–2 upon comparing the top waveform with the

samples in the bottom plot. The synchronization required to sample at the proper instant is no

small problem, but will be considered to be carried out ideally in this example. In the next

section, we consider a more detailed block diagram than Figure 1–1 and explain the different

operations that may be encountered in a digital communications system.

1.2 Objectives


• Give brief introduction to Digital Data Transmission.

1.3 Components of a Digital Communications System

The mechanization and performance considerations for digital communications systems

will now be discussed in more detail. Figure 1–3 shows a system block diagram that is more

detailed than that of Figure 1–1. The functions of all the blocks of Figure 1–3 are discussed in

this section.

1.3.1 General Considerations

In most communication system designs, a general objective is to use the resources of

bandwidth and transmitted power as efficiently as possible. In many applications, one of these

resources is scarcer than the other, which results in the classification of most channels as either

bandwidth limited or power limited. Thus we are interested in both a transmission scheme’s

bandwidth efficiency, defined as the ratio of data rate to signal bandwidth, and its power

efficiency, characterized by the probability of making a reception error as a function of signal-to-

noise ratio. We give a preliminary discussion of this power-bandwidth efficiency trade-off in

Section 1.4.3. Often, secondary restrictions may

for example, the waveform at the output

properties in order to accommodate

(TWTA).

1.3.2 Subsystems in a Typical Communication System

We now briefly consider each set of blocks in Figure 1

partner at the receiving end. Consider first the source and sink blocks. As previously

the discrete information source can be the result of desiring to transmit a natu

FIGURE 1–3 Block diagram of a typical digital communication system.

discrete alphabet of characters or the desire to transmit the output of an analog source digitally. If

the latter is the case, the analog source, assumed lowpass of bandwidth W hertz i

discussion, is sampled and each sample quantized. In order to recover the signal from its

samples, according to the sampling theorem , the sampling rate fs must obey the Nyquist

criterion, which is

fs ≥ 2W samples / seconds

.3. Often, secondary restrictions may be imposed in choosing a transmission method,

e waveform at the output of the data modulator may be required to have certain

properties in order to accommodate nonlinear amplifiers such as a traveling-wave tube amplifier

.2 Subsystems in a Typical Communication System

r each set of blocks in Figure 1–3, one at the transmitting end and

partner at the receiving end. Consider first the source and sink blocks. As previously

the discrete information source can be the result of desiring to transmit a naturally

3 Block diagram of a typical digital communication system.


the latter is the case, the analog source, assumed lowpass of bandwidth W hertz i



≥ 2W samples / seconds (1–1)

be imposed in choosing a transmission method,

of the data modulator may be required to have certain

wave tube amplifier

3, one at the transmitting end and its

partner at the receiving end. Consider first the source and sink blocks. As previously discussed,

rally

3 Block diagram of a typical digital communication system.


the latter is the case, the analog source, assumed lowpass of bandwidth W hertz in this



Furthermore, if each sample is quantized into q levels, then log2 q bits are required to represent

each sample value and the minimum source rate in this case is

Rm= (fs )min log 2 q = 2W log2 q bits/ second (1–2)

Consider next the source encoder and decoder blocks in Figure 1–3. Most sources possess

redundancy, manifested by dependencies between successive symbols or by the probabilities of

occurrence of these symbols not being equal, in their outputs. It is therefore possible to represent

a string of symbols, each one being selected from an alphabet of q symbols, from the output of a

redundant source by fewer than log2 q bits per symbol on the average. Thus the function of the

source encoder and decoder blocks in Figure 1–3 is to remove redundancy before transmission

and decode the reduced-redundancy symbols at the receiver, respectively.

It is often desirable to make the transmissions secure from unwanted interceptors. This is the

function of the encryptor and decryptor blocks shown in Figure 1–3. This is true not only in

military applications, but many civilian applications as well (consider the undesirability, for

example, of a competitor learning the details of a competing bid for a construction project that is

being sent to a potential customer by means of a public carrier transmission system). Although

much of the literature on this subject is classified, provides an excellent overview.

In many communications systems, it might not be possible to achieve the level of transmission

reliability desired with the transmitter and receiver parameters available (e.g., power, bandwidth,

receiver sensitivity, and modulation technique). A way to improve performance in many cases is

to encode the transmitted data sequence by adding redundant symbols and using this redundancy

to detect and correct errors at the receiver output. This is the function of the channel

encoder/decoder blocks shown in Figure 1–3. It may seem strange that redundancy is now added

after removing redundancy with the source encoder. This is reasonable, however, since the

channel encoder adds controlled redundancy, which the channel decoder makes use of to correct

errors, whereas the redundancy removed by the source encoder is uncontrolled and is difficult to

make use of in.

1.5 Summary

Data transmitted may be digital messages originating from a data source, for example a computer

or a keyboard. It may also be an analog signal such as a phone call or a video

signal, digitized into a bit-stream for example using pulse-code modulation (PCM) or more

advanced source coding (analog-to-digital conversion and data compression) schemes. This

source coding and decoding is carried out by codec equipment.

1.6 Keywords

• Digital Data Transmission

• Waveform

• FEC

• TWTA

1.7 Exercise

1. Give brief introduction to Digital Data Transmission.

Unit 2

Representation of Data Signal

Structure

2.1 Introduction

2.2 Objectives

2.3 Data

2.4 Signal

2.5 Signal Characteristics

2.6 Digital Signal

2.7 Baseband and Broadband Signals

2.8 Summary

2.9 Keywords

2.10 Exercise

2.1 Introduction

A simplified model of a data communication system is shown in Fig. 2.1.1. Here there

are five basic components:

Source: Source is where the data is originated. Typically it is a computer, but it can be any other

electronic equipment such as telephone handset, video camera, etc, which can generate data for

transmission to some destination. The data to be sent is represented by x(t).

Figure 2.1.1 Simplified model of a data communication system

Transmitter: As data cannot be sent in its native form, it is necessary to convert it into signal.

This is performed with the help of a transmitter such as modem. The signal that is sent by the

transmitter is represented by s(t).

Communication Medium: The signal can be sent to the receiver through a communication

medium, which could be a simple twisted-pair of wire, a coaxial cable, optical fiber or wireless

communication system. It may be noted that the signal that comes out of the communication

medium is s’(t), which is different from s(t) that was sent by the transmitter. This is due to

various impairments that the signal suffers as it passes through the communication medium.

Receiver: The receiver receives the signal s’(t) and converts it back to data d’(t) before

forwarding to the destination. The data that the destination receives may not be identical to that

of d(t), because of the corruption of data.

Destination: Destination is where the data is absorbed. Again, it can be a computer system, a

telephone handset, a television set and so on.

2.2 Objectives


• Explain what is data

• Distinguish between Analog and Digital signal

• Explain the difference between time and Frequency domain representation of signal

• Specify the bandwidth of a signal

• Specify the Sources of impairment

• Explain Attenuation and Unit of Attenuation

• Explain Data Rate Limits and Nyquist Bit Rate

• Distinguish between Bit Rate and Baud Rate

• Identify Noise Sources

2.3 Data

Data refers to information that conveys some meaning based on some mutually agreed up

rules or conventions between a sender and a receiver and today it comes in a variety of forms

such as text, graphics, audio, video and animation.

Data can be of two types; analog and digital. Analog data take on continuous values on some

interval. Typical examples of analog data are voice and video. The data that are collected from

the real world with the help of transducers are continuous-valued or analog in nature. On the

contrary, digital data take on discrete values. Text or character strings can be considered as

examples of digital data. Characters are represented by suitable codes, e.g. ASCII code, where

each character is represented by a 7-bit code.

2.4 Signal

It is electrical, electronic or optical representation of data, which can be sent over a

communication medium. Stated in mathematical terms, a signal is merely a function of the data.

For example, a microphone converts voice data into voice signal, which can be sent over a pair

of wire. Analog signals are continuous-valued; digital signals are discrete-valued. The

independent variable of the signal could be time (speech, for example), space (images), or the

integers (denoting the sequencing of letters and numbers in the football score). Figure 2.1.2

shows an analog signal.

Figure 2.1.2 Analog signal

Digital signal can have only a limited number of defined values, usually two values 0 and 1, as

shown in Fig. 2.1.3.

Figure 2.1.3 Digital signal

Signaling: It is an act of sending signal over communication medium

Transmission: Communication of data by propagation and processing is known as transmission.

2.5 Signal Characteristics

A signal can be represented as a function of time, i.e. it varies with time. However, it can

be also expressed as a function of frequency, i.e. a signal can be considered as a composition of

different frequency components. Thus, a signal has both time-domain and frequency domain

representation.

2.5.1 Time-domain concepts

A signal is continuous over a period, if

limt->a s (t) = s (a), for all a,

i.e., there is no break in the signal. A signal is discrete if it takes on only a finite number of

values. A signal is periodic if and only if

s (t+T) = s (t) for - α < t < α ,

where T is a constant, known as period. The period is measured in seconds.

In other words, a signal is a periodic signal if it completes a pattern within a measurable time

frame. A periodic signal is characterized by the following three parameters.

Amplitude: It is the value of the signal at different instants of time. It is measured in volts.

Frequency: It is inverse of the time period, i.e. f = 1/T. The unit of frequency is Hertz (Hz) or

cycles per second.

Phase: It gives a measure of the relative position in time of two signals within a single period. It

is represented by φ in degrees or radian.

A sine wave, the most fundamental periodic signal, can be completely characterized by its

amplitude, frequency and phase. Examples of sine waves with different amplitude, frequency

and phase are shown in Fig. 2.1.4. The phase angle φ indicated in the figure is with respect to the

reference waveform shown in Fig. 2.1.4(a).

Figure 2.1.4 Examples of signals with different amplitude, frequency and phase

An aperiodic signal or nonperiodic signal changes constantly without exhibiting a pattern or

cycle that repeats over time as shown in Fig. 2.1.5.

Figure 2.1.5

Examples of signals with different amplitude, frequency and phase

or nonperiodic signal changes constantly without exhibiting a pattern or

peats over time as shown in Fig. 2.1.5.

Figure 2.1.5 Examples of aperiodic signals

Examples of signals with different amplitude, frequency and phase

or nonperiodic signal changes constantly without exhibiting a pattern or

2.5.2 Frequency domain concepts

The time domain representation displays a signal using time-domain plot, which shows

changes in signal amplitude with time. The time-domain plot can be visualized with the help of

an oscilloscope. The relationship between amplitude and frequency is provided by frequency

domain representation, which can be displayed with the help of spectrum analyser. Time domain

and frequency domain representations of three sine waves of three different frequencies are

shown in Fig. 2.1.6.

Figure 2.1.6 Time domain and frequency domain representations of sine waves

Although simple sine waves help us to understand the difference between the time-domain and

frequency domain representation, these are of little use in data communication. Composite

signals made of many simple sine waves find use in data communication. Any composite signal

can be represented by a combination of simple sine waves using Fourier Analysis. For example,

the signal shown in Fig. 2.1.7(c) is a composition of two sine waves having frequencies f1, 3f1,

shown in Fig. 2.1.7 (a) and (b), respectively and it can be represented by

s (t) = sin ωt + 1/3 sin 3ωt , where ω = 2πf1.

The frequency domain function s(f) specifies the constituent frequencies of the signal. The range

of frequencies that a signal contains is known as it spectrum, which can be visualized with the

help of a spectrum analyser. The band of frequencies over which most of the energy of a signal is

concentrated is known as the bandwidth of the signal.

Figure 2.1.7 Time and frequency domain representations of a composite signal

Many useful waveforms don’t change in a smooth curve between maximum and minimum

amplitude; they jump, slide, wobble, spike, and dip. But as long as these irregularities are

consistent, cycle after cycle, a signal is still periodic and logically must be describable in same

terms used for sine waves. In fact it can be decomposed into a collection of sine waves, each

having a measurable amplitude, frequency, and phase.

2.5.3 Frequency Spectrum

Frequency spectrum of a signal is the range of frequencies that a signal contains.

Example: Consider a square wave shown in Fig. 2.1.8(a). It can be represented by a series of sine

waves S(t) = 4A/πsin2πft + 4A/3πsin(2π(3f)t) + 4A/5πsin2π (5f)t + . . . having frequency

components f, 3f, 5f, … and amplitudes 4A/π, 4A/3π, 4A/5π and so on. The frequency spectrum

of this signal can be approximation comprising only the first and third harmonics as shown in

Fig. 2.1.8(b)

(a)

(b)

Figure 2.1.8 (a) A square wave, (b) Frequency spectrum of a square wave

Bandwidth: The range of freque

contained is known as bandwidth

somewhat arbitrary. Usually, it is defined in terms of its 3dB cut

spectrum and spectrum of a signal is shown in Fig. 2.1.9. Here the fl and fh may be represented

by 3dB below (A/√2) the maximum amplitude.

Figure 2.1.9 Frequency spectrum and bandwidth of a signal

2.6 Digital Signal

In addition to being represented by an analog signal, data can be also be represented by a

digital signal. Most digital signals are a

Two new terms, bit interval (instead of period) and

describe digital signals. The bit interval is the time required to send one single bit. The bit rate is

the number of bit interval per second. This mean that the bit rate is the number of bits send in

one second, usually expressed in bits per second (bps) as shown in Fig. 2.1.10.

Figure 2.1.10

The range of frequencies over which most of the signal energy of a signal is

bandwidth or effective bandwidth of the signal. The term ‘most’ is

somewhat arbitrary. Usually, it is defined in terms of its 3dB cut-off frequency. The frequency

spectrum of a signal is shown in Fig. 2.1.9. Here the fl and fh may be represented

2) the maximum amplitude.

Frequency spectrum and bandwidth of a signal


digital signal. Most digital signals are a periodic and thus, period or frequency is not appropriate.

(instead of period) and bit rate (instead of frequency) are used to



expressed in bits per second (bps) as shown in Fig. 2.1.10.

Figure 2.1.10 Bit Rate and Bit Interval

ncies over which most of the signal energy of a signal is

or effective bandwidth of the signal. The term ‘most’ is

off frequency. The frequency

spectrum of a signal is shown in Fig. 2.1.9. Here the fl and fh may be represented


periodic and thus, period or frequency is not appropriate.

(instead of frequency) are used to



A digital signal can be considered as a signal with an infinite number of frequencies and

transmission of digital requires a low-pass channel as shown in Fig. 2.1.11. On the other hand,

transmission of analog signal requires band-pass channel shown in Fig. 2.1.12.

Figure 2.1.11 Low pass channel required for transmission of digital signal

Figure 2.1.12 Low pass channel required for transmission of analog signal

Digital transmission has several advantages over analog transmission. That is why there is a shift

towards digital transmission despite large analog base. Some of the advantages of digital

transmission are highlighted below:

• Analog circuits require amplifiers, and each amplifier adds distortion and noise to the

signal. In contrast, digital amplifiers regenerate an exact signal, eliminating cumulative

errors. An incoming (analog) signal is sampled, its value is determined, and the node then

generates a new signal from the bit value; the incoming signal is discarded. With analog

circuits, intermediate nodes amplify the incoming signal, noise and all.

• Voice, data, video, etc. can all by carried by digital circuits. What about carrying digital

signals over analog circuit? The modem example shows the difficulties in carrying digital

over analog. A simple encoding method is to use constant voltage levels for a “1'' and a

``0''. Can lead to long periods where the voltage does not change.

• Easier to multiplex large channel capacities with digital.

• Easy to apply encryption to digital data.

• Better integration if all signals are in one form. Can integrate voice, video and digital

data.

2.7 Baseband and Broadband Signals

Depending on some type of typical signal formats or modulation schemes, a few

terminologies evolved to classify different types of signals. So, we can have either a base band or

broadband signalling. Base-band is defined as one that uses digital signalling, which is inserted

in the transmission channel as voltage pulses. On the other hand, broadband systems are those,

which use analog signalling to transmit information using a carrier of high frequency.

In baseband LANs, the entire frequency spectrum of the medium is utilized for transmission and

hence the frequency division multiplexing (discussed later) cannot be used. Signals inserted at a

point propagates in both the directions, hence transmission is bi-directional. Baseband systems

extend only to limited distances because at higher frequency, the attenuation of the signal is most

pronounced and the pulses blur out, causing the large distance communication totally

impractical.

Since broadband systems use analog signalling, frequency division multiplexing is possible,

where the frequency spectrum of the cable is divided into several sections of bandwidth. These

separate channels can support different types of signals of various frequency ranges to travel at

the same instance. Unlike base-band, broadband is a unidirectional medium where the signal

inserted into the media propagates in only one direction. Two data paths are required, which are

connected at a point in the network called headend. All the stations transmit towards the headend

on one path and the signals received at the headend are propagated through the second path.

2.8 Summary

Data refers to information that conveys some meaning based on some mutually agreed up

rules or conventions between a sender and a receiver and today it comes in a variety of forms

such as text, graphics, audio, video and animation. It is electrical, electronic or optical

representation of data, which can be sent over a communication medium.

A signal can be represented as a function of time, i.e. it varies with time. However, it can

be also expressed as a function of frequency, i.e. a signal can be considered as a composition of

different frequency components. Thus, a signal has both time-domain and frequency domain

representation.

2.9 Keywords

• Source

• Transmitter

• Communication Medium

• Receiver

• Destination

• Signal

• Amplitude

• Frequency

• Phase

2.10 Exercise

1. Distinguish between data and signal.

2. What do you mean by a “Periodic Signal”? And what are the three parameters that

characterize it?

3. Distinguish between time domain and frequency domain representation of a signal.

4. What equipments are used to visualize electrical signals in time domain and frequency

domain?

5. What do you mean by the Bit Interval and Bit rate in a digital signal?

Unit 3

Digital Data Transmission-1

Structure

3.1 Introduction

3.2 Objectives

3.3 Parallel and Serial Data Transmission

3.4 20ma Loop and Line Drivers

3.5 Modems

3.6 Summary

3.7 Keywords

3.8 Exercise

3.1 Introduction

The transmission mode refers to the number of elementary units of information (bits)

that can be simultaneously translated by the communications channel. In fact, processors (and

therefore computers in general) never process (in the case of recent processors) a single bit at a

time; generally they are able to process several (most of the time it is 8: one byte), and for this

reason the basic connections on a computer are parallel connections.

3.2 Objectives


• Know the Parallel and Serial Data Transmission.

• Explain 20ma Loop And Line Drivers.

• Know how Modem works.

3.3 Parallel and Serial Data Transmission

Digital data transmission can occur in two basic modes: serial or parallel. Data within

a computer system is transmitted via parallel mode on buses with the width of the parallel

bus matched to the word size of the computer system. Data between computer systems is usually

transmitted in bit serial mode. Consequently, it is necessary to make a parallel-to-serial

conversion at a computer interface when sending data from a computer system into a network

and a serial-to-parallel conversion at a computer interface when receiving information from a

network. The type of transmission mode used may also depend upon distance and required data

rate.

Parallel Transmission

In parallel transmission, multiple bits (usually 8 bits or a byte/character) are sent simultaneously

on different channels (wires, frequency channels) within the same cable, or radio path,

and synchronized to a clock. Parallel devices have a wider data bus than serial devices and can

therefore transfer data in words of one or more bytes at a time. As a result, there is a speedup in

parallel transmission bit rate over serial transmission bit rate. However, this speedup is a tradeoff

versus cost since multiple wires cost more than a single wire, and as a parallel cable gets longer,

the synchronization timing between multiple channels becomes more sensitive to distance.

The timing for parallel transmission is provided by a constant clocking signal sent over a

separate wire within the parallel cable; thus parallel transmission is considered synchronous.

Serial Transmission

In serial transmission, bits are sent sequentially on the same channel (wire) which reduces

costs for wire but also slows the speed of transmission. Also, for serial transmission, some

overhead time is needed since bits must be assembled and sent as a unit and then disassembled at

the receiver.

Serial transmission can be either synchronous or asynchronous. In synchronous transmission,

groups of bits are combined into frames and frames are sent continuously with or without data to

be transmitted. In asynchronous transmission, groups of bits are sent as independent units with

start/stop flags and no data link synchronization, to allow for arbitrary size gaps between frames.

However, start/stop bits maintain physical bit level synchronization once detected.

Applications

Serial transmission is between two computers or from a computer to an external device located

some distance away. Parallel transmission either takes place within a computer system (on a

computer bus) or to an external device located a close distance away.

A special computer chip known as a universal asynchronous receiver transmitter (UART) acts as

the interface between the parallel transmission of the computer bus and the serial transmission of

the serial port. UARTs differ in performance capabilities based on the amount of on-chip

memory they possess.

Examples

Examples of parallel mode transmission include connections between a computer and a printer

(parallel printer port and cable). Most printers are within6 meters or 20 feet of the transmitting

computer and the slight cost for extra wires is offset by the added speed gained through

parallel transmission of data.

Examples of serial mode transmission include connections between a computer and a modem

using the RS-232 protocol. Although an RS-232 cable can theoretically accommodate 25 wires,

all but two of these wires are for overhead control signaling and not data transmission; the two

data wires perform simple serial transmission in either direction. In this case, a computer may

not be close to a modem, making the cost of parallel transmission prohibitive—thus speed

of transmission may be considered less important than the economical advantage of

serial transmission.

Tradeoffs

Serial transmission via RS-232 is officially limited to 20 Kbps for a distance of 15 meters or 50

feet. Depending on the type of media used and the amount of external interference present, RS-

232 can be transmitted at higher speeds, or over greater distances, or both.

Parallel transmission has similar distance-versus-speed tradeoffs, as well as a clocking threshold

distance. Techniques to increase the performance of serial and parallel transmission (longer

distance for same speed or higher speed for same distance) include using

better transmission media, such as fiber optics or conditioned cables, implementing repeaters, or

using shielded/multiple wires for noise immunity.

Technology

To resolve the speed and distance limitations of serial transmission via RS-232, several other

serial transmission standards have been developed including RS-449, V.35, Universal Serial Bus

(USB), and IEEE-1394 (Fire wire). Each of these standards has different electrical, mechanical,

functional, and procedural characteristics. The electrical characteristics define voltage levels

and timing of voltage level changes. Mechanical characteristics define the actual connector shape

and number of wires. Common mechanical interface standards associated with

parallel transmission are the DB-25 and Centronics connectors. The Centronics connector is a

36-pin parallel interface that also defines electrical signaling. Functional characteristics specify

the operations performed by each pin in a connector; these can be classified into the broad

categories of data, control, timing, and electrical ground. The procedural characteristics or

protocol define the sequence of operations performed by pins in the connector.

3.4 20ma Loop and Line Drivers

For digital serial communications, a current loop is a communication interface that

uses current instead of voltage for signaling. Current loops can be used over moderately long

distances (tens of kilo metres), and can be interfaced with optically isolated links.

Long before the RS-232 standard, current loops were used to send digital data

in serial form for teleprinters. More than two teletypes could be connected on a single circuit

allowing a simple form of networking. Older teletypes used a 60 mA current loop. Later

machines, such as the ASR33 teleprinter, operated on a lower 20 mA current level and most

early minicomputers featured a 20 mA current loop interface, with an RS-232 port generally

available as a more expensive option. The original IBM PC serial port card had provisions for a

20 mA current loop. A digital current loop uses the absence of current for high (space or break),

and the presence of current in the loop for low (mark).

The maximum resistance for a current loop is limited by the available voltage. Current

loop interfaces usually use voltages much higher than those found on anRS-232 interface, and

cannot be interconnected with voltage-type inputs without some form of level translator circuit.

MIDI (Musical Instrument Digital Interface) is a digital current loop interface.

Process Control use

For industrial process control instruments, analog 4–20 mA and 10–50 mA current loops

are commonly used for analog signaling, with 4 mA representing the lowest end of the range and

20 mA the highest. The key advantages of the current loop are that the accuracy of the signal is

not affected by voltage drop in the interconnecting wiring, and that the loop can supply operating

power to the device. Even if there is significant electrical resistance in the line, the current loop

transmitter will maintain the proper current, up to its maximum voltage capability. The live-

zero represented by 4 mA allows the receiving instrument to detect some failures of the loop, and

also allows transmitter devices to be powered by the same current loop (called two-

wire transmitters). Such instruments are used to measure pressure, temperature, flow, pH or other

process variables. A current loop can also be used to control a valve positioner or other

output actuator. An analog current loop can be converted to a voltage input with a precision

resistor. Since input terminals of instruments may have one side of the current loop input tied to

the chassis ground (earth), analog isolators may be required when connecting several instruments

in series.

Depending on the source of current for the loop

power) or passive (relying on loop power). For example, a

power to a pressure transmitter. The pr

send the signal to the strip chart recorder, but does not in itself supply power to the loop and so is

passive. (A 4-wireinstrument has a power supply input separate from the current loop.) Another

loop may contain two passive chart recorders, a passive pressure transmitter, and a 24 V battery.

(The battery is the active device).

Panel mount displays and chart recorders are commonly termed 'indicator devices' or 'process

monitors'. Several passive indicator devices may be connected in series, but a loop must have

only one transmitter device and only one power source (active device).

The relationship between current value and process variable measurement is set by calibration,

which assigns different ranges of engineering units to the span between 4 and 20

mapping between engineering units and current can be inverted, so that 4

maximum and 20 mA the minimum.

Depending on the source of current for the loop, devices may be classified as active

(relying on loop power). For example, a chart recorder may provide loop

power to a pressure transmitter. The pressure transmitter modulates the current on the loop to


instrument has a power supply input separate from the current loop.) Another

op may contain two passive chart recorders, a passive pressure transmitter, and a 24 V battery.

(The battery is the active device).


cator devices may be connected in series, but a loop must have

only one transmitter device and only one power source (active device).


ges of engineering units to the span between 4 and 20

mapping between engineering units and current can be inverted, so that 4 mA represents the

mA the minimum.

Typ 2

active (supplying

may provide loop

essure transmitter modulates the current on the loop to


instrument has a power supply input separate from the current loop.) Another

op may contain two passive chart recorders, a passive pressure transmitter, and a 24 V battery.


cator devices may be connected in series, but a loop must have


ges of engineering units to the span between 4 and 20 mA. The

mA represents the

Typ 3

Typ 4

3.5 Modems

A modem (from modulate and demodulate) is a device that modulates an analog carrier

signal to encode digital information, and also demodulates such a carrier signal to decode the

transmitted information. The goal is to produce a signal that can be transmitted easily and

decoded to reproduce the original digital data. Modems can be used over any means of

transmitting analog signals, from driven diodes to radio.

The most familiar example is a voice band modem that turns the digital '1s and 0s' of a personal

computer into sounds that can be transmitted over the telephone lines of Plain Old Telephone

Systems (POTS), and once received on the other side, converts those 1s and 0s back into a form

used by a USB, Serial, or Network connection. Modems are generally classified by the amount

of data they can send in a given time, normally measured in bits per second, or "bps."

Faster modems are used by Internet users every day, notably cable modems and ADSL modems.

In telecommunications, "radio modems" transmit repeating frames of data at very high data rates

over microwave radio links. Some microwave modems transmit more than a hundred million bits

per second. Optical modems transmit data over optical fibers. Most intercontinental data links

now use optical modems transmitting over undersea optical fibers. Optical modems routinely

have data rates in excess of a billion (1x109) bits per second.

The working of the modems

Modem is an abbreviation for Modulator Demodulator. A modem converts data from digital

computer signals to analog signals that can be sent over a phone line (modulation). The analog

signals are then converted back into digital data by the receiving modem (demodulation). A

modem is given digital information in the form of ones and zeros by the computer. The modem

converts it to analog signals and sends over the phone line. Another modem then receives these

signals, converts them back into digital data and sends the data to the receiving computer.

The actual process is much more complicated then it seems. Here we discuss some internal

functions of modem that helps in the modulation and demodulation process.

1. Data Compression

Computers are capable of transmitting information to modems much faster than the modems are

able to transmit the same information over a phone line. However, in order to transmit data at a

speed greater than 600 bits per second (bps), it is necessary for modems to collect bits of

information together and transmit them via a more complicated sound. This allows the

transmission of many bits of data at the same time. This gives the modem time to group bits

together and apply compression algorithms to them. Modem compresses them and sends over.

2. Error Correction

Error correction is the method by which modems verify if the information sent to them has been

undamaged during the transfer. Error correcting modems break up information into small

packets, called frames and send over after adding a checksum to each of these frames. The

receiving modem checks whether the checksum matches the information sent. If not, the entire

frame is resent. Though error correction data transfer integrity is preserved.

3. Flow Control

If one modem in a dial up connection is capable of sending data much faster than the other can

receive then flow control allows the receiving modem to tell the other to pause while it catches

up. Flow control exists as either software or hardware flow control. With software flow control,

when a modem needs to tell the other to pause, it sends a certain character signaling pause. When

it is ready to resume, it sends a different character. Since software flow control regulates

transmissions by sending certain characters, line noise could generate the character commanding

a pause, thus hanging the transfer until the proper character is sent. Hardware flow control uses

wires in the modem cable. This is faster and much more reliable than software flow control.

4. Data Buffering

Data buffering is done using a UART. A UART (Universal Asynchronous

Receiver/Transmitters) is an integrated circuit that converts parallel input into serial output.

UART is used by computers to send information to a serial device such as a modem. The

computer communicates with the serial device by writing in the UART's registers. UARTs have

buffers through which this communication occurs on First in First out basis. It means that the

first data to enter the buffer is the first to leave. Without the FIFO, information would be

scrambled when sent by a modem. This basically helps the CPU to catch up if it has been busy

dealing with other tasks.

Data Transmission via Modem

Early approach: use existing telephony network for data transmission

• Problem of transferring digital data over an analogous medium

• Necessary: usage of a Modem (Modulator - Demodulator)

• Digital data are transformed in analogous signals with different frequencies (300 to

3400 Hz, range of voice transmitted over telephony network). The analogous signals are

brought to the receiver over the telephony network. The receiver also needs a modem to

transform back the analogous signals into digital data.

• For the telephony network the modem seems to be a normal phone, the modem even

takes over the exchange of signaling information

• Data rate up to 56 kBit/s

• High susceptibility against transmission errors due to telephony cables

Modulation of Digital Signals

The digital signals (0 resp. 1) have to be transformed into electromagnetic signals, that process

is called modulation

Modulation means to choose a carrier frequency and “press”

3.6 Summary

There are two methods of transmitting digital

serial transmissions. In parallel data transmission, all bits of the binary data are transmitted

simultaneously. For example, to transmit an 8

another, eight transmission lines are required


Modulation means to choose a carrier frequency and “press” on somehow your data:

There are two methods of transmitting digital data. These methods are parallel and


, to transmit an 8-bit binary number in parallel from one unit to

lines are required. Each bit requires its own separate


on somehow your data:

data. These methods are parallel and


parallel from one unit to

Each bit requires its own separate data path. All

bits of a word are transmitted at the same time. This method of transmission can move a

significant amount of data in a given period of time. Its disadvantage is the large number

of interconnecting cables between the two units. For large binary words, cabling becomes

complex and expensive. This is particularly true if the distance between the two units is great.

Long multi wire cables are not only expensive, but also require special interfacing to minimize

noise and distortion problems. The 4-2OmA current loop has been with us for so long that it's

become rather taken for granted in the industrial and process sectors alike. Its popularity comes

from its ease of use and its performance. However, just because something is that ubiquitous

doesn't mean we're all necessarily getting the best out of our current loops.

3.7 Keywords

• Modem

• Buses

• Bits

• Serial Transmission

• Modulate

• Demodulate

• Flow Control

3.8 Exercise

1. Explain the Parallel and Serial Data Transmission.

2. Explain 20ma Loop And Line Drivers.

3. Explain the working of Modem.

Unit 4

Digital Data Transmission-2

Structure

4.1 Introduction

4.2 Objectives

4.3 Transient Noise Pulses

4.4 Data Signal: Signal Shaping And Signaling Speed

4.5 Partial Response (Correlative) Techniques

4.6 Repeaters

4.7 Summary

4.8 Keywords

4.9 Exercise

4.1 Introduction

Noise can be defined as an unwanted signal that interferes with the communication or

measurement of another signal. A noise itself is a signal that conveys information regarding the

source of the noise. For example, the noise from a car engine conveys information regarding the

state of the engine. The sources of noise are many, and vary from audio frequency acoustic noise

emanating from moving, vibrating or colliding sources such as revolving machines, moving

vehicles, computer fans, keyboard clicks, wind, rain, etc. to radio-frequency electromagnetic

noise that can interfere with the transmission and reception of voice, image and data over the

radio-frequency spectrum. Signal distortion is the term often used to describe a systematic

undesirable change in a signal and refers to changes in a signal due to the non–ideal

characteristics of the transmission channel, reverberations, echo and missing samples.

4.2 Objectives


• Know the Transient Noise Pulses.

• Explain Signal Shaping.

• Explain the Repeaters.

4.3 Transient Noise Pulses

Transient noise pulses often consist of a relatively short sharp initial pulse followed by

decaying low-frequency oscillations as shown in Figure 1.1. The initial pulse is usually due to

some external or internal impulsive interference, whereas the oscillations are often due to the

resonance of the

Figure 1.1 (a) A scratch pulse and music from a gramophone record. (b) The averaged profile of

a gramophone record scratch

communication channel excited by the initial pulse, and may be considered as the response of the

channel to the initial pulse. In a telecommunication system, a noise pulse originates at some

point in time and space, and then propagates through the c

is shaped by the channel characteristics, and may be considered as the channel pulse response.

Thus we should be able to characterize the transient noise pulses with a similar degree of

consistency as in characterizing the channels through which the pulses propagate.

As an illustration of the shape of a transient noise pulse, consider the scratch pulses from a

damaged gramophone record shown in Figures 1.1(a) and (b). Scratch noise pulses are acoustic

manifestations of the response of the stylus and the associated electro

system to a sharp physical discontinuity on the recording medium. Since scratches are essentially

the impulse response of the playback mechanism, it is expected that for a given s

scratch pulses exhibit a similar characteristics. As shown in Figure 1.1(b), a typical scratch pulse

waveform often exhibits two distinct regions:

(a) the initial high-amplitude pulse response of the playback system to the physical

discontinuity on the record medium, followed by;

(b) decaying oscillations that cause additive distortion. The initial pulse is relatively short

and has a duration on the order of 1

duration and may last up to 50


a gramophone record scratch pulse.



point in time and space, and then propagates through the channel to the receiver. The noise pulse



ng the channels through which the pulses propagate.



of the response of the stylus and the associated electro-mechanical playback


the impulse response of the playback mechanism, it is expected that for a given s


waveform often exhibits two distinct regions:

amplitude pulse response of the playback system to the physical

inuity on the record medium, followed by;


and has a duration on the order of 1–5 ms, whereas the oscillatory tail has a longer

duration and may last up to 50 ms or more.




hannel to the receiver. The noise pulse



ng the channels through which the pulses propagate.



mechanical playback


the impulse response of the playback mechanism, it is expected that for a given system, various


amplitude pulse response of the playback system to the physical


5 ms, whereas the oscillatory tail has a longer

Note in Figure 1.1(b) that the frequency of the decaying oscillations decreases with time. This

behaviour may be attributed to the non-linear modes of response of the electro-mechanical

playback system excited by the physical scratch discontinuity. Observations of many scratch

waveforms from damaged gramophone records reveals that they have a well-defined profile, and

can be characterised by a relatively small number of typical templates.

4.4 Data Signal: Signal Shaping and Signaling Speed

In digital telecommunication, pulse shaping is the process of changing the waveform of

transmitted pulses. Its purpose is to make the transmitted signal better suited to

the communication channel by limiting the effective bandwidth of the transmission. By filtering

the transmitted pulses this way, the inter symbol interference caused by the channel can be kept

in control. In RF communication, pulse shaping is essential for making the signal fit in its

frequency band.

Need for pulse shaping

Transmitting a signal at high modulation rate through a band-limited channel can

create intersymbol interference. As the modulation rate increases, the signal's bandwidth

increases. When the signal's bandwidth becomes larger than the channel bandwidth, the channel

starts to introduce distortion to the signal. This distortion is usually seen as intersymbol

interference.

The signal's spectrum is determined by the pulse shaping filter used by the transmitter. Usually

the transmitted symbols are represented as a time sequence of dirac delta pulses. This theoretical

signal is then filtered with the pulse shaping filter, producing the transmitted signal. The

spectrum of the transmission is thus determined by the filter.

In many base band communication systems the pulse shaping filter is implicitly a boxcar filter.

Its spectrum is of the form sin(x)/x, and has significant signal power at frequencies higher than

symbol rate. This is not a big problem when optical fibre or even twisted pair cable is used as the

communication channel. However, in RF communications this would waste bandwidth, and only

tightly specified frequency bands are used for single transmissions. In other words, the channel

for the signal is band-limited. Therefore better filters have been developed, which attempt to

minimise the bandwidth needed for a certain symbol rate.

Pulse filters

Not all filters can be used as a pulse shaping filter. The filter itself must not introduce

intersymbol interference — it needs to satisfy certain criteria. Nyquist ISI criterion is commonly

used criterion for evaluation of filters, because it relates the frequency spectrum of the

transmitter signal to intersymbol interference.

Examples of pulse-shaping filters that are commonly found in communication systems are:

The trivial boxcar filter

Sinc shaped filter

Raised-cosine filter

Gaussian filter

Sender side pulse shaping is often combined with a receiver side matched filter to achieve

optimum tolerance for noise in the system. In this case the pulse shaping is equally distributed to

the sender and receiver filters. The filters' amplitude responses are thus point wise square-roots

of the system filters.

Other approaches that eliminate complex pulse shaping filters have been invented. In OFDM, the

carriers are modulated so slowly that each carrier is virtually unaffected by the bandwidth

limitation of the channel.

Boxcar filter :The boxcar filter results in infinitely wide bandwidth for the signal. Thus its

usefulness is limited, but it is used widely in wired baseband communications, where the channel

has some extra bandwidth and the distortion created by the channel can be tolerate

Sinc filter: Theoretically the best pulse shaping filter would be the sinc filter, but it cannot be

implemented precisely. It is a non

problematic from a synchronisation point of view as any phase error results in steeply increasing

intersymbol interference.

Raised-cosine filter: Raised-cosine filter is practical to implement and it is in wide use. It has a

parametrisable excess bandwidth, so communication systems can choose a trade

more complex filter and spectral efficiency.

Gaussian filter: This gives an output pulse shaped like a

boxcar filter results in infinitely wide bandwidth for the signal. Thus its


has some extra bandwidth and the distortion created by the channel can be tolerate

Theoretically the best pulse shaping filter would be the sinc filter, but it cannot be

non-causal filter with relatively slowly decaying tails. It is also


cosine filter is practical to implement and it is in wide use. It has a

ametrisable excess bandwidth, so communication systems can choose a trade

more complex filter and spectral efficiency.

This gives an output pulse shaped like a Gaussian function.

boxcar filter results in infinitely wide bandwidth for the signal. Thus its


has some extra bandwidth and the distortion created by the channel can be tolerated.

Theoretically the best pulse shaping filter would be the sinc filter, but it cannot be

ying tails. It is also


cosine filter is practical to implement and it is in wide use. It has a

ametrisable excess bandwidth, so communication systems can choose a trade-off between a

4.5 Partial Response (Correlative) Techniques

The Nyquist criteria for binary and multi-level signaling, postulated in 1924, are based on the

premise that each digit must be confined to its own time slot to as great an extent as possible.

This implies that the intersymbol interference (ISI) in a particular time interval, due to the tails of

preceding and succeeding pulses, should be eliminated or, at least, minimized. The Nyquist rate

cannot be achieved in practice, even if the ideal rectangular filter were synthesized, because it is

not possible to have a precise relationship between the cut-off frequency of the ideal filter and

the bit rate. Thus, the Nyquist rate with the Nyquist-type zero-memory system cannot be

achieved. Correlative techniques introduce, deliberately, a limited amount of ISI over a span of

one, two, or more digits and capitalize on it. The net result is spectral reshaping of binary or

multi-level pulse trains. The consequences are significant: For a given bandwidth and power

input to the channel, correlative techniques permit the transmission of substantially more bits per

second per hertz (b/s/Hz) than Nyquist-type zero-memory systems, for a specified probability of

error criterion. With correlative techniques, the Nyquist rate and higher rates are possible. Also,

owing to correlation between digits, correlative pulse trains have distinctive patterns. These

patterns are monitored at the receiver; any violations due to noise or other causes result in errors

which may be easily detected. Thus, error detection is accomplished without introducing

redundant bits, such as parity checks, at the transmitter.

4.6 Repeaters

A repeater for a transmission system which can pass signals in either of two directions.

Each direction has a signal detection circuit associated with it. Upon detection of the beginning

of a signal, the signal detection circuit enables an associated driver to pass the signal in the

appropriate direction and at the same time disables the other signal detection circuit so that a

signal will pass in only one direction at a time. An end flag detecting circuit monitors for certain

characteristics associated with the end of the signal, and upon detection causes both drivers to be

disabled and both signal detection circuits to be reset so that they can again detect a signal

passing in either direction.

1) In digital communication systems, a repeater is a device that receives

a digital signal on an electromagnetic or optical transmission medium and regenerates the

signal along the next leg of the medium. In electromagnetic media, repeaters overcome

the attenuationcaused by free-space electromagnetic-field divergence or cable loss. A

series of repeaters make possible the extension of a signal over a distance.

Repeaters remove the unwanted noise in an incoming signal. Unlike an analog signal, the

original digital signal, even if weak or distorted, can be clearly perceived and restored.

With analog transmission, signals are restrengthened with amplifiers which unfortunately

also amplify noise as well as information.

Because digital signals depend on the presence or absence of voltage, they tend to

dissipate more quickly than analog signals and need more frequent repeating. Whereas

analog signal amplifiers are spaced at 18,000 meter intervals, digital signal repeaters are

typically placed at 2,000 to 6,000 meter intervals.

2) In a wireless communications system, a repeater consists of a radio receiver, an

amplifier, a transmitter, an isolator, and two antennas. The transmitter produces a signal

on a frequency that differs from the received signal. This so-called frequency offset is

necessary to prevent the strong transmitted signal from disabling the receiver. The

isolator provides additional protection in this respect. A repeater, when strategically

located on top of a high building or a mountain, can greatly enhance the performance of a

wireless network by allowing communications over distances much greater than would

be possible without it.

3) In satellite wireless, a repeater (more frequently called a transponder) receives uplink

signals and retransmits them, often on different frequencies, to destination locations.

4) In a cellular telephone system, a repeater is one of a group of transceivers in a

geographic area that collectively serve a system user.

5) In a fiber optic network, a repeater consists of a photocell, an amplifier, and a light-

emitting diode (LED) or infrared-emitting diode (IRED) for each light or IR signal that

requires amplification. Fiber optic repeaters operate at power levels much lower than

wireless repeaters, and are also much simpler and cheaper. However, their design

requires careful attention to ensure that internal circuit noise is minimized.

6) Repeaters are commonly used by commercial and amateur radio operators to extend

signals in the radio frequency range from one receiver to another. These consist of drop

repeaters, similar to the cells in cellular radio, and hub repeaters, which receive and

retransmit signals from and to a number of directions.

7) A bus repeater links one computer bus to a bus in another computer chassis,

essentially chaining one computer to another.

4.7 Summary

In digital telecommunication, pulse shaping is the process of changing the waveform of

transmitted pulses. Its purpose is to make the transmitted signal better suited to

the communication channel by limiting the effective bandwidth of the transmission. By filtering

the transmitted pulses this way, the intersymbol interference caused by the channel can be kept in

control. In RF communication, pulse shaping is essential for making the signal fit in its

frequency band. A repeater for a transmission system which can pass signals in either of two

directions. Each direction has a signal detection circuit associated with it. Upon detection of the

beginning of a signal, the signal detection circuit enables an associated driver to pass the signal

in the appropriate direction and at the same time disables the other signal detection circuit so that

a signal will pass in only one direction at a time.

4.8 Keywords

• Radio-frequency

• Signal Shaping

• Repeaters.

• Pulse shaping

• Pulse filters

4.9 Exercise

1. Explain the Transient Noise Pulses .

2. Explain Signal Shaping.

3. Explain the Repeaters.

Unit 1

Digital Modulation System-1

Structure

1.1 Introduction

1.2 Objectives

1.3 Digital Modulation System

1.4 Phase-shift keying

1.5 Summary

1.6 Keywords

1.7 Exercise

1.1 Introduction

Firstly, what do we mean by digital modulation? Typically the objective of a digital

communication system is to transport digital data between two or more nodes. In radio

communications this is usually achieved by adjusting a physical characteristic of a sinusoidal

carrier, the frequency, phase, amplitude or a combination thereof. This is performed in real

systems with a modulator at the transmitting end to impose the physical change to the carrier and

a demodulator at the receiving end to detect the resultant modulation on reception.

1.2 Objectives


• Explain Digital Modulation System

• Know the Digital Modulation techniques.

• Explain Phase-shift keying.

1.3 Digital Modulation System

The techniques used to modulate digital information so that it can be transmitted via

microwave, satellite or down a cable pair is different to that of analogue transmission. The data

transmitted via satellite or microwave is transmitted as an analogue signal. The techniques used

to transmit analogue signals are used to transmit digital signals. The problem is to convert the

digital signals to a form that can be treated as an analogue signal that is then in the appropriate

form to either be transmitted down a twisted cable pair or applied to the RF stage where is

modulated to a frequency that can be transmitted via microwave or satellite.

The equipment that is used to convert digital signals into analogue format is a modem. The word

modem is made up of the words “modulator” and “demodulator”.

A modem accepts a serial data stream and converts it into an analogue format that matches the

transmission medium.

There are many different modulation techniques that can be utilised in a modem. These

techniques are:

• Amplitude shift key modulation (ASK)

• Frequency shift key modulation (FSK)

• Binary-phase shift key modulation (BPSK)

• Quadrature-phase shift key modulation (QPSK)

• Quadrature amplitude modulation (QAM)

The most common digital modulation techniques are:

1. Phase-shift keying (PSK):

a. Binary PSK (BPSK), using M=2 symbols

b. Quadrature PSK (QPSK), using M=4 symbols

c. Differential PSK (DPSK)

2. Frequency-shift keying (FSK):

a. Audio frequency-shift keying (AFSK)

b. Multi-frequency shift keying (M-ary FSK or MFSK)

3. Amplitude-shift keying (ASK)

4. Quadrature amplitude modulation (QAM) - a combination of PSK and ASK:

5. Wavelet modulation

6. Spread-spectrum techniques:

a. Direct-sequence spread spectrum (DSSS)

b. Chirp spread spectrum (CSS) according to IEEE 802.15.4a CSS uses pseudo-

stochastic coding

c. Frequency-hopping spread spectrum (FHSS) applies a special scheme for channel

release

1.4 Phase-shift keying

Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing,

or modulating, the phase of a reference signal (the carrier wave).

Any digital modulation scheme uses a finite number of distinct signals to represent digital data.

PSK uses a finite number of phases, each assigned a unique pattern of binary bits. Usually, each

phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented

by the particular phase. The demodulator, which is designed specifically for the symbol-set used

by the modulator, determines the phase of the received signal and maps it back to the symbol it

represents, thus recovering the original data.

(a) Binary phase-shift keying (BPSK)

BPSK (also sometimes called PRK, Phase Reversal Keying, or 2PSK) is the simplest

form of phase shift keying (PSK). It uses two phases which are separated by 180° and so can also

be termed 2-PSK. It does not particularly matter exactly where the constellation points are

positioned, and in this figure they are shown on the real axis, at 0° and 180°. This modulation is

the most robust of all the PSKs since it takes the highest level of noise or distortion to make the

demodulator reach an incorrect decision. It is, however, only able to modulate at 1 bit/symbol (as

seen in the figure) and so is unsuitable for high data-rate applications when bandwidth is limited.

Implementation

Binary data is often conveyed with the following signals:

for binary "0"

for binary "1"

where fc is the frequency of the carrier-wave.

Hence, the signal-space can be represented by the single basis function

where 1 is represented by and 0 is represented by . This assignment is, of course, arbitrary.

The use of this basis function is shown at the end of the next section in a signal timing diagram.

The topmost signal is a BPSK-modulated cosine wave that the BPSK modulator would produce.

The bit-stream that causes this output is shown above the signal (the other parts of this figure are

relevant only to QPSK).

Bit error rate

The bit error rate (BER) of BPSK in AWGN can be calculated as[5]

:

or

Since there is only one bit per symbol, this is also the symbol error rate.

(b) Quadrature phase-shift keying (QPSK)

Constellation diagram for QPSK with Gray coding. Each adjacent symbol only differs by

one bit. Sometimes known as quaternary or quadriphase PSK, 4-PSK, or 4-QAM[6]

, QPSK uses

four points on the constellation diagram, equispaced around a circle. With four phases, QPSK

can encode two bits per symbol. Analysis shows that this may be used either to double the data

rate compared to a BPSK system while maintaining the bandwidth of the signal or to maintain

the data-rate of BPSK but halve the bandwidth needed.

As with BPSK, there are phase ambiguity problems at the receiver and differentially encoded

QPSK is used more often in practice.

Implementation

The implementation of QPSK is more general than that of BPSK and also indicates the

implementation of higher-order PSK. Writing the symbols in the constellation diagram in terms

of the sine and cosine waves used to transmit them:

This yields the four phases π/4, 3π/4, 5π/4 and 7π/4 as needed. This results in a two-

dimensional signal space with unit basis functions. The first basis function is used as the in-phase

component of the signal and the second as the quadrature component of the signal.

Hence, the signal constellation consists of the signal-space 4 points. The factors of 1/2 indicate

that the total power is split equally between the two carriers. Comparing these basis functions

with that for BPSK shows clearly how QPSK can be viewed as two independent BPSK signals.

Note that the signal-space points for BPSK do not need to split the symbol (bit) energy over the

two carriers in the scheme shown in the BPSK constellation diagram.

QPSK systems can be implemented in a number of ways. An illustration of the major

components of the transmitter and receiver structure are shown below.

Conceptual transmitter structure for QPSK. The binary data stream is split into the in-

phase and quadrature-phase components. These are then separately modulated onto two

orthogonal basis functions. In this implementation, two sinusoids are used. Afterwards, the two

signals are superimposed, and the resulting signal is the QPSK signal. Note the use of polar non-

return-to-zero encoding. These encoders can be placed before for binary data source, but have

been placed after to illustrate the conceptual difference between digital and analog signals

involved with digital modulation.

Receiver structure for QPSK. The matched filters can be replaced with correlators. Each

detection device uses a reference threshold value to determine whether a 1 or 0 is detected.

Bit error rate

Although QPSK can be viewed as a quaternary modulation, it is easier to see it as two

independently modulated quadrature carriers. With this interpretation, the even (or odd) bits are

used to modulate the in-phase component of the carrier, while the odd (or even) bits are used to

modulate the quadrature-phase component of the carrier. BPSK is used on both carriers and they

can be independently demodulated.

As a result, the probability of bit-error for QPSK is the same as for BPSK:

However, in order to achieve the same bit-error probability as BPSK, QPSK uses twice the

power (since two bits are transmitted simultaneously).

The symbol error rate is given by:

If the signal-to-noise ratio is high (as is necessary for practical QPSK systems) the probability of

symbol error may be approximated:

QPSK signal in the time domain

The modulated signal is shown below for a short segment of a random binary data-stream. The

two carrier waves are a cosine wave and a sine wave, as indicated by the signal-space analysis

above. Here, the odd-numbered bits have been assigned to the in-phase component and the even-

numbered bits to the quadrature component (taking the first bit as number 1). The total signal —

the sum of the two components — is shown at the bottom. Jumps in phase can be seen as the

PSK changes the phase on each component at the start of each bit-period. The topmost waveform

alone matches the description given for BPSK above.

The binary data that is conveyed by this waveform is: 1 1 0 0 0 1 1 0.

• The odd bits, highlighted here, contribute to the in-phase component: 1 1 0 0 0 1 1 0

• The even bits, highlighted here, contribute to the quadrature-phase component: 1 1 0 0 0

1 1 0

(c) Differential phase-shift keying (DPSK)

Differential phase shift keying (DPSK) is a common form of phase modulation that conveys data

by changing the phase of the carrier wave. As mentioned for BPSK and QPSK there is an

ambiguity of phase if the constellation is rotated by some effect in the communications channel

through which the signal passes. This problem can be overcome by using the data to change

rather than set the phase.

For example, in differentially-encoded BPSK a binary '1' may be transmitted by adding 180° to

the current phase and a binary '0' by adding 0° to the current phase. In differentially-encoded

QPSK, the phase-shifts are 0°, 90°, 180°, -90° corresponding to data '00', '01', '11', '10'. This kind

of encoding may be demodulated in the same way as for non-differential PSK but the phase

ambiguities can be ignored. Thus, each received symbol is demodulated to one of the M

points in the constellation and a comparator then computes the difference in phase between this

received signal and the preceding one. The difference encodes the data as described above.

The modulated signal is shown below for both DBPSK and DQPSK as described above. It is

assumed that the signal starts with zero phase, and so there is a phase shift in both signals at t

= 0 .

Analysis shows that differential encoding approximately doubles the error rate compared to

ordinary M -PSK but this may be overcome by only a small increase in E b /

N 0 . Furthermore, this analysis (and the graphical results below) are based on a system in

which the only corruption is additive white Gaussian noise. However, there will also be a

physical channel between the transmitter and receiver in the communication system. This

channel will, in general, introduce an unknown phase-shift to the PSK signal; in these cases the

differential schemes can yield a better error-rate than the ordinary schemes which rely on precise

phase information.

Demodulation

For a signal that has been differentially encoded, there is an obvious alternative method of

demodulation. Instead of demodulating as usual and ignoring carrier-phase ambiguity, the phase

between two successive received symbols is compared and used to determine what the data must

have been. When differential encoding is used in this manner, the scheme is known as

differential phase-shift keying (DPSK). Note that this is subtly different to just differentially-

encoded PSK since, upon reception, the received symbols are not decoded one-by-one to

constellation points but are instead compared directly to one another.

Call the received symbol in the kth

timeslot r k and let it have phase φ k . Assume

without loss of generality that the phase of the carrier wave is zero. Denote the AWGN term as

n k . Then

.

The decision variable for the k − 1th

symbol and the kth

symbol is the phase

difference between r k and r k − 1 . That is, if r k is projected

onto r k − 1 , the decision is taken on the phase of the resultant complex number:

where superscript * denotes complex conjugation. In the absence of noise, the phase of this is

θ k − θ k − 1 , the phase-shift between the two received signals which can be

used to determine the data transmitted.

The probability of error for DPSK is difficult to calculate in general, but, in the case of DBPSK it

is:

which, when numerically evaluated, is only slightly worse than ordinary BPSK, particularly at

higher E b / N 0 values.

Using DPSK avoids the need for possibly complex carrier-recovery schemes to provide an

accurate phase estimate and can be an attractive alternative to ordinary PSK.

In optical communications, the data can be modulated onto the phase of a laser in a differential

way. For the case of BPSK for example, the laser transmits the field unchanged for binary '1',

and with reverse polarity for '0'. In further processing, a photo diode is used to transform the

optical field into an electric current, so the information is changed back into its original state.

The bit-error rates of DBPSK and DQPSK are compared to their non-differential counterparts in

the graph to the right. For DQPSK though, the loss in performance compared to ordinary QPSK

is larger and the system designer must balance this against the reduction in complexity.

1.5 Summary

This section covers the main digital modulation formats, their main applications, relative

spectral efficiencies, and some variations of the main modulation types as used in practical

systems. Fortunately, there are a limited number of modulation types which form the building

blocks of any system.

1.6 Keywords

• Digital information

• Analogue transmission

• modem

• Modulator

• Demodulator

• ASK

• FSK

• BPSK

• QPSK

• QAM

• QAM

• DSSS

• CSS

• FHSS

1.7 Exercise

1. Explain Digital Modulation System.

2. List the Digital Modulation techniques.

3. Explain Phase-shift keying.

Unit 2

Digital Modulation System-2

Structure

1.1 Introduction

1.2 Objectives

1.3. Frequency-shift keying

1.4. Amplitude-shift keying

1.5. Quadrature amplitude modulation

1.6 Summary

1.7 keywords

1.8 Exercise

1.1 Introduction

The choice of digital modulation scheme will significantly affect the characteristics,

performance and resulting physical realisation of a communication system. There is no universal

'best' choice of scheme, but depending on the physical characteristics of the channel, required

levels of performance and target hardware trade-offs, some will prove a better fit than others.

Consideration must be given to the required data rate, acceptable level of latency, available

bandwidth, anticipated link budget and target hardware cost, size and current consumption. The

physical characteristics of the channel, be it hardwired without the associated problems of

fading, or a mobile communications system to a F1 racing car with fast changing multipath, will

typically significantly affect the choice of optimum system.

1.2 Objectives


• Explain Frequency-shift keying.

• Explain Amplitude-shift keying.

• Explain Quadrature amplitude modulation.

1.3. Frequency-shift keying

Frequency-shift keying (FSK) is a frequency modulation scheme in which digital

information is transmitted through discrete frequency changes of a carrier wave. The simplest

FSK is binary FSK (BFSK). BFSK literally implies using a couple of discrete frequencies to

transmit binary (0s and 1s) information. With this scheme, the "1" is called the mark frequency

and the "0" is called the space frequency.

Other forms of FSK

Minimum-shift keying

Main article: Minimum-shift keying

Minimum frequency-shift keying or minimum-shift keying (MSK) is a particularly spectrally

efficient form of coherent FSK. In MSK the difference between the higher and lower frequency

is identical to half the bit rate. Consequently, the waveforms used to represent a 0 and a 1 bit

differ by exactly half a carrier period. This is the smallest FSK modulation index that can be

chosen such that the waveforms for 0 and 1 are orthogonal. A variant of MSK called GMSK is

used in the GSM mobile phone standard.

FSK is commonly used in Caller ID and remote metering applications: see FSK standards for use

in Caller ID and remote metering for more details.

Audio FSK

Audio frequency-shift keying (AFSK) is a modulation technique by which digital data is

represented by changes in the frequency (pitch) of an audio tone, yielding an encoded signal

suitable for transmission via radio or telephone. Normally, the transmitted audio alternates

between two tones: one, the "mark", represents a binary one; the other, the "space", represents a

binary zero.

AFSK differs from regular frequency-shift keying in performing the modulation at baseband

frequencies. In radio applications, the AFSK-modulated signal normally is being used to

modulate an RF carrier (using a conventional technique, such as AM or FM) for transmission.

AFSK is not always used for high-speed data communications, since it is far less efficient in both

power and bandwidth than most other modulation modes. In addition to its simplicity, however,

AFSK has the advantage that encoded signals will pass through AC-coupled links, including

most equipment originally designed to carry music or speech.

1.4. Amplitude-shift keying

Amplitude-shift keying (ASK) is a form of modulation that represents digital data as

variations in the amplitude of a carrier wave.

The amplitude of an analog carrier signal varies in accordance with the bit stream (modulating

signal), keeping frequency and phase constant. The level of amplitude can be used to represent

binary logic 0s and 1s. We can think of a carrier signal as an ON or OFF switch. In the

modulated signal, logic 0 is represented by the absence of a carrier, thus giving OFF/ON keying

operation and hence the name given.

Like AM, ASK is also linear and sensitive to atmospheric noise, distortions, propagation

conditions on different routes in PSTN, etc. Both ASK modulation and demodulation processes

are relatively inexpensive. The ASK technique is also commonly used to transmit digital data

over optical fiber. For LED transmitters, binary 1 is represented by a short pulse of light and

binary 0 by the absence of light. Laser transmitters normally have a fixed "bias" current that

causes the device to emit a low light level. This low level represents binary 0, while a higher-

amplitude lightwave represents binary 1.

Encoding

The simplest and most common form of ASK operates as a switch, using the presence of a

carrier wave to indicate a binary one and its absence to indicate a binary zero. This type of

modulation is called on-off keying, and is used at radio frequencies to transmit Morse code

(referred to as continuous wave operation).

More sophisticated encoding schemes have been developed which represent data in groups using

additional amplitude levels. For instance, a four-level encoding scheme can represent two bits

with each shift in amplitude; an eight-level scheme can represent three bits; and so on. These

forms of amplitude-shift keying require a high signal-to-noise ratio for their recovery, as by their

nature much of the signal is transmitted at reduced power.

Here is a diagram showing the ideal model for a transmission system using an ASK modulation

It can be divided into three blocks. The first one represents the transmitter, the second one is a

linear model of the effects of the channel, the third one shows the structure of the receiver. The

following notation is used:

• ht(t) is the carrier signal for the transmission

• hc(t) is the impulse response of the channel

• n(t) is the noise introduced by the channel

• hr(t) is the filter at the receiver

• L is the number of levels that are used for transmission

• Ts is the time between the generation of two symbols

Different symbols are represented with different voltages. If the maximum allowed value for the

voltage is A, then all the possible values are in the range [-A,A] and they are given by:

the difference between one voltage and the other is:

Considering the picture, the symbols v[n] are generated randomly by the source S, then the

impulse generator creates impulses with an area of v[n]. These impulses are sent to the filter ht

to be sent through the channel. In other words, for each symbol a different carrier wave is sent

with the relative amplitude.

Out of the transmitter, the signal s(t) can be expressed in the form:

In the receiver, after the filtering through hr (t) the signal is:

where we use the notation:

n r ( t ) = n ( t ) *

h r ( t )

g ( t ) = h t ( t ) *

h c ( t ) * h r ( t )

where * indicates the convolution between two signals. After the A/D conversion the signal z[k]

can be expressed in the form:

In this relationship, the second term represents the symbol to be extracted. The others are

unwanted: the first one is the effect of noise, the second one is due to the intersymbol

interference.

If the filters are chosen so that g(t) will satisfy the Nyquist ISI criterion, then there will be no

intersymbol interference and the value of the sum will be zero, so:

z [ k ] = n r [ k ] +

v [ k ] g [ 0 ]

the transmission will be affected only by noise.

Probability of error

The probability density function to make an error after a certain symbol has been sent can be

modelled by a Gaussian function; the mean value will be the relative sent value, and its variance

will be given by:

where Φ N ( f ) is the spectral density of the noise within the band and Hr (f) is

the continuous Fourier transform of the impulse response of the filter hr (f).

The possibility to make an error is given by:

where is the conditional probability of making an error after a symbol vi has been sent and is the

probability of sending a symbol v0.

If the probability of sending any symbol is the same, then:

If we represent all the probability density functions on the same plot against the possible value of

the voltage to be transmitted, we get a picture like this (the particular case of L=4 is shown):

The possibility of making an error after a single symbol has been sent is the area of the Gaussian

function falling under the other ones. It is shown in cyan just for one of them. If we call P+ the

area under one side of the Gaussian, the sum of all the areas will be: 2 L P +

− 2 P +

. The total probability of making an error can be expressed in the

form:

We have now to calculate the value of P+. In order to do that, we can move the origin of the

reference wherever we want: the area below the function will not change. We are in a situation

like the one shown in the following picture:

it does

not matter which Gaussian function we are considering, the area we want to calculate will be the

same. The value we are looking for will be given by the following integral:

where erfc() is the complementary error function. Putting all these results together, the

probability to make an error is:

from this formula we can easily understand that the probability to make an error decreases if the

maximum amplitude of the transmitted signal or the amplification of the system becomes

greater; on the other hand, it increases if the number of levels or the power of noise becomes

greater.

1.5. Quadrature amplitude modulation

Quadrature amplitude modulation (QAM) is both an analog and a digital modulation

scheme. It conveys two analog message signals, or two digital bit streams, by changing

(modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital

modulation scheme or amplitude modulation (AM) analog modulation scheme. These two

waves, usually sinusoids, are out of phase with each other by 90° and are thus called quadrature

carriers or quadrature components — hence the name of the scheme. The modulated waves are

summed, and the resulting waveform is a combination of both phase-shift keying (PSK) and

amplitude-shift keying, or in the analog case of phase modulation (PM) and amplitude

modulation. In the digital QAM case, a finite number of at least two phases, and at least two

amplitudes are used. PSK modulators are often designed using the QAM principle, but are not

considered as QAM since the amplitude of the modulated carrier signal is constant.

Digital QAM

Like all modulation schemes, QAM conveys data by changing some aspect of a carrier signal, or

the carrier wave, (usually a sinusoid) in response to a data signal. In the case of QAM, the

amplitude of two waves, 90 degrees out-of-phase with each other (in quadrature) are changed

(modulated or keyed) to represent the data signal. Amplitude modulating two carriers in

quadrature can be equivalently viewed as both amplitude modulating and phase modulating a

single carrier.

Phase modulation (analog PM) and phase-shift keying (digital PSK) can be regarded as a special

case of QAM, where the magnitude of the modulating signal is a constant, with only the phase

varying. This can also be extended to frequency modulation (FM) and frequency-shift keying

(FSK), for these can be regarded as a special case of phase modulation.

Analog QAM

When transmitting two signals by modulating them with QAM, the transmitted signal will be of

the form:

where I ( t ) and Q ( t ) are the modulating signals and f 0 is the

carrier frequency.

At the receiver, these two modulating signals can be demodulated using a coherent demodulator.

Such a receiver multiplies the received signal separately with both a cosine and sine signal to

produce the received estimates of I ( t ) and Q ( t ) respectively.

Because of the orthogonality property of the carrier signals, it is possible to detect the

modulating signals independently.

In the ideal case I ( t ) is demodulated by multiplying the transmitted signal with a

cosine signal:

Using standard trigonometric identities, we can write it as:

Low-pass filtering r i ( t ) removes the high frequency terms (containing

4 π f 0 t ), leaving only the I ( t ) term. This filtered signal is

unaffected by Q ( t ) , showing that the in-phase component can be received

independently of the quadrature component. Similarly, we may multiply s ( t ) by a

sine wave and then low-pass filter to extract Q ( t ) .

The phase of the received signal is assumed to be known accurately at the receiver. This issue of

carrier synchronization at the receiver must be handled somehow in QAM systems. The coherent

demodulator needs to be exactly in phase with the received signal, or otherwise the modulated

signals cannot be independently received. For example analog television systems transmit a burst

of the transmitting colour subcarrier after each horizontal synchronization pulse for reference.

Analog QAM is used in NTSC and PAL television systems, where the I- and Q-signals carry the

components of chroma (colour) information. "Compatible QAM" or C-QUAM is used in AM

stereo radio to carry the stereo difference information.

Fourier analysis of QAM

In the frequency domain, QAM has a similar spectral pattern to DSB-SC modulation. Using the

properties of the Fourier transform, we find that:

where S(f), MI(f) and MQ(f) are the Fourier transforms (frequency-domain representations) of s(t),

I(t) and Q(t), respectively

1.6 Summary

The objective of this chapter is to review the key characteristics and salient features of

the main digital modulation schemes used, including consideration of the receiver and

transmitter requirements. Simulation is used to compare the performance and tradeoffs of three

popular systems, MSK, GMSK and BPSK, including analysis of key parameters such as

occupied bandwidth and Bit Error Rate (BER) in the presence of Additive White Gaussian Noise

(AWGN). Finally the digital modulation schemes used in the current and proposed cellular

standards are summarised.

1.7 keywords

• FSK

• BFSK

• MSK

• Audio FSK

• AM or FM

• ASK

• LED

• QAM

• Fourier analysis of QAM

1.8 Exercise

1. Explain Frequency-shift keying.

2. Explain Amplitude-shift keying.

3. Explain Quadrature amplitude modulation.

Unit 3

Communication Over band limited channels

Structure

3.1 Introduction

3.2 Objectives

3.3 Bandlimited channels

3.4 Digital Signaling Through Bandlimited Awgn Channels

3.5 Equalization Techniques

3.6 Further Discussion

3.7 Summary

3.8 Keywords

3.9 Exercise

3.1 Introduction

Thus far in this course, we have been treating the communication channel as having no

effect on the signal, or at worst simply as attenuating the transmitted signal by some known

factor. Thus, the energy E that has been the subject of much discussion could be referred to as

the received energy (which is what it is) or as the transmitted energy since the two quantities

were identical, or at worst, had a known linear relationship. If we were to model such a channel

as a linear time-invariant system with impulse response g(t), then g(t) would be taken to be δ(t)

where δ(t) denotes the unit impulse.

Thus, the channel output would be the same as the input, or the input attenuated by a

factor α . In practice, all channels change the transmitted signal in ways other than simple

attenuation, but when the channel has bandwidth much larger than that of the transmitted signal,

and G(f) is essentially a constant over the frequency band of interest, then it is a reasonable

approximation to model g(t) as δ(t) or α*δ(t). Otherwise, when the channel transfer function

varies significantly over the frequency band of interest, the e effect of the channel on the

transmitted signal needs to be taken into account. Such channels are called band-limited or

bandwidth-limited channels and they cause a phenomenon called inter symbol interference. As

the name implies, inter symbol interference (ISI) means that each sample value in the receiver

depends not just on the symbol being demodulated but also on other symbols being transmitted.

The presence of these extraneous symbols interferes with the demodulation process. For

example, the designs for optimum receivers for signals received over AWGN channels that we

have been studying thus far do not take ISI into account at all, and when ISI is present, their

performance can be quite poor. In this Lecture and the next few, we shall study how ISI arises,

and how to to mitigate its effects on the performance of communication systems operating over

band-limited channels.

3.2 Objectives


• Explain Band limited channels.

• Know Digital Signaling Through Bandlimited Awgn Channels.

• Give Equalization Techniques.

3.3 Bandlimited channels

Another cause of intersymbol interference is the transmission of a signal through

a bandlimited channel, i.e., one where the frequency response is zero above a certain frequency

(the cutoff frequency). Passing a signal through such a channel results in the removal of

frequency components above this cutoff frequency; in addition, the amplitude of the frequency

components below the cutoff frequency may also be attenuated by the channel.

This filtering of the transmitted signal affects the shape of the pulse that arrives at the receiver.

The effects of filtering a rectangular pulse; not only change the shape of the pulse within the first

symbol period, but it is also spread out over the subsequent symbol periods. When a message is

transmitted through such a channel, the spread pulse of each individual symbol will interfere

with following symbols.

As opposed to multipath propagation, bandlimited channels are present in both wired and

wireless communications. The limitation is often imposed by the desire to operate multiple

independent signals through the same area/cable; due to this, each system is typically allocated a

piece of the total bandwidth available. For wireless systems, they may be allocated a slice of

the electromagnetic spectrum to transmit in (for example, FM radio is often broadcast in the

87.5 MHz - 108 MHz range). This allocation is usually administered by a government agency; in

the case of the United Statesthis is the Federal Communications Commission (FCC). In a wired

system, such as an optical fiber cable, the allocation will be decided by the owner of the cable.

The bandlimiting can also be due to the physical properties of the medium - for instance, the

cable being used in a wired system may have a cutoff frequency above which practically none of

the transmitted signal will propagate.

Communication systems that transmit data over bandlimited channels usually implement pulse

shaping to avoid interference caused by the bandwidth limitation. If the channel frequency

response is flat and the shaping filter has a finite bandwidth, it is possible to communicate with

no ISI at all. Often the channel response is not known beforehand, and an adaptive equalizer is

used to compensate the frequency response.

3.4 Optimum Pulse Shape Design for Digital Signaling Through

Bandlimited Awgn Channels

We treat digital communication over a channel that is modeled as a linear filter with a

bandwidth limitation. The bandwidth constrain generally precludes the use of rectangular pulses

at the output of the modulator. Instead, the transmitted signals must be shaped to restrict their

bandwidth to that available on the channel. The channel distortion results in intersymbol

interference (ISI) at the output of the demodulator and leads to an increase in the probability of

error at the detector. Devices or methods for correcting or undoing the channel distortion, called

channel equalizers.

A bandlimited channel is characterized as a linear filter with impulse response c(t) and frequency

response c(f),

If the channel is a baseband that is bandlimited to Bc ,then

Suppose that the input to a bandlimited channel is a signal waveform g

of the channel is the convolution of g

Expressed in the frequency domain, we have

If the channel is a baseband that is bandlimited to Bc ,then

C(f)=0 for |f|> Bc

Suppose that the input to a bandlimited channel is a signal waveform gT(t). Then the response

of the channel is the convolution of gT(t) with c(t) ;i.e.,

Expressed in the frequency domain, we have

H(f)=C(f)GT(f)

(t). Then the response

The signal at the input to the demodulator is of the form h(t)+n(t), where n(t) denotes the

AWGN. Let us pass the received signal h(t)+n(t) through the matched filter that has a frequency

response

where t0 is some nominal time delay at which we sample the filter output.

The signal component at the output of the matched filter at the sampling instant t=t

The noise component at the output of the matched filter has a zero mean and a power

density

The noise power at the output of the matched filter has a

The SNR at the output of the matched filter is

input to the demodulator is of the form h(t)+n(t), where n(t) denotes the


is some nominal time delay at which we sample the filter output.

The signal component at the output of the matched filter at the sampling instant t=t

The noise component at the output of the matched filter has a zero mean and a power

The noise power at the output of the matched filter has a variance

The SNR at the output of the matched filter is

input to the demodulator is of the form h(t)+n(t), where n(t) denotes the


The signal component at the output of the matched filter at the sampling instant t=t0 is

The noise component at the output of the matched filter has a zero mean and a power-spectral

Compared to the previous result, the major difference in this development is that the filter

impulse response is matched to the received signal h(t) instead of the transmitted signal.

3.5 Equalization Techniques

Due to the distortive character of the propagation environment, transmitted data symbols

will spread out in time and will interfere with each other, a phenomenon called Inter Symbol

Interference (ISI). The degree of ISI depends on the data rate: the higher the data rate, the more

ISI is introduced. On the other hand, changes in the propagation environment, e.g., due to

mobility in wireless communications, introduce channel time-variation, which could be very

harmful.

Mitigating these fading channel effects, also referred to as channel equalization,

constitutes a major challenge in current and future communication systems. In order to design a

good channel equalizer, a practical channel model has to be derived. First of all, we can write the

overall system as a symbol rate Single-Input Multiple-Output (SIMO) system, where the

multiple outputs are obtained by multiple receive antennas and/or fractional sampling. Then,

looking at a fixed time-window, we can distinguish between Time-InVariant (TIV) and Time-

Varying (TV) channels. For TIV channels, we will model the channel by a TIV FIR channel,

whereas for TV channels, it will be convenient to model the channel time-variation by means of

a Basis Expansion Model (BEM), leading to a BEM FIR channel [40], [14], [33]. For TIV

channels, channel equalizers have been extensively studied in literature (see for instance [30, ch.

10], [19, ch. 10], [15, ch. 5], [12] and references therein). For TV channels, on the other hand,

they have only been introduced recently. Instead of focusing on complex Maximum Likelihood

(ML) or Maximum A Posteriori (MAP) equalizers, we will discuss more practical finite-length

linear and decision feedback equalizers. We derive Minimum Mean-Square Error (MMSE)

solutions, which strike an optimal balance between ISI removal and noise enhancement.

By setting the signal power to infinity, these MMSE solutions can easily be transformed into

Zero-Forcing (ZF) solutions that completely remove the ISI. We mainly focus on equalizer

design based on channel knowledge, and briefly mention channel estimation algorithms and

direct equalizer design algorithms, which do not require channel knowledge.

3.6 Further Discussion

Further Abstract-Continuous-time additive white Gaussian noise channels with strictly

time-limited and root-mean-square (RMS) bandlimited inputs are studied. RMS bandwidth is

equal to the normalized second moment of the spectrum, which has proved to be a useful and

analytically tractable measure of the bandwidth of strictly time-limited waveforms. The capacity

of the single-user and two-user RMS-bandlimited channels are found in easy-to-compute

parametric forms, and are compared to the classical formulas for the capacity of strictly

bandlimited channels. In addition, channels are considered where the inputs are further

constrained to be pulse amplitude modulated (PAM) waveforms. The capacity of the single-user

RMS-bandlimited PAM channel is shown to coincide with Shannon’s capacity formula for the

strictly bandlimited channel. This shows that the laxer bandwidth constraint precisely offsets the

PAM structural constraint, and illustrates a tradeoff between the time domain and frequency

domain constraints. In the synchronous two-user channel, we find the pair of pulses that achieves

the boundary of the capacity region, and show that the shapes of the optimal pulses depend not

only on the bandwidth but also on the respective signal-to-noise ratios. Index Terms-Bandlimited

communication, information rate, multiuser channels.

3.7 Summary

The designs for optimum receivers for signals received over AWGN channels that we

have been studying thus far do not take ISI into account at all, and when ISI is present, their

performance can be quite poor. In this Lecture and the next few, we shall study how ISI arises,

and how to to mitigate its effects on the performance of communication systems operating over

band-limited channels.

Communication systems that transmit data over bandlimited channels usually implement pulse

shaping to avoid interference caused by the bandwidth limitation. If the channel frequency

response is flat and the shaping filter has a finite bandwidth, it is possible to communicate with

no ISI at all. Often the channel response is not known beforehand, and an adaptive equalizer is

used to compensate the frequency response.

3.8 Keywords

• ISI

• MHz

• SIMO

• TIV

• BEM

• MMSE

• ZF

• RMS

• PAM

3.9 Exercise

1. Explain Band limited channels.

2. Explain Digital Signaling Through Bandlimited Awgn Channels.

3. Give Equalization Techniques.

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