Chapter 6: Introduction to Digital Communicationmyweb.utem.edu.my/myweb/noorazwan/Chapter_6.pdf · high-frequency analog carriers are modulated by relatively low ... forms of digital

Chapter 6: Introduction to Digital Communication

BENT 3113: Communication Principles

93


6.1 Introduction

In the context of this course, digital communications include systems where relatively

high-frequency analog carriers are modulated by relatively low-frequency digital

information signals (digital modulation) and systems involving the transmission of digital

pulses (digital transmission). Digital transmission systems transport information in digital

form therefore they require a physical facility between the transmitter and receiver such

as a metallic wire pair, a coaxial cable or an optical fiber cable. In digital modulation

systems, the carrier facility could be a physical cable or it could be free space.

In this chapter, the student will be first introduced to information theory parameters

followed by the introduction of several forms of digital modulation system. The final part

of the chapter is where the student will learn more on digital transmission systems.

6.2 Information Theory Parameters

6.2.1 Information Capacity, Bits and Bit Rate

Information theory is a study of the efficient use of bandwidth to propagate information

through electronic communication systems. Information theory can be used to determine

the information capacity of a data communication system.

Information capacity is a measure of how much information can be propagated through a

communication system and it is a function of bandwidth and transmission time.

• I.e. information capacity represents the number of independent symbols that can

be carried through a system in a given unit of time.

• The most basic digital symbol used to represent information is the binary digit, or

bit.

• Bit rate is simply the number of bits transmitted during one second and is

expressed in bits per second (bps).

In 1928, Hartley’s Law is developed to show the relation between information capacity,

bandwidth and transmission time.

• Hartley Law:

tBI ×∝ (6.1)

Where I = information capacity (bps)

B = bandwidth (Hz)

t = transmission time (seconds)



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Then in 1948, mathematician Claude E. Shannon relates the information capacity of a

communication channel to bandwidth and signal-to-noise ratio. The higher the signal-to-

noise ratio, the higher the information capacity is. I.e. better performance is produced.

• Shannon limit for information capacity:

+=

N

SBI 1log 2 or

+=

N

SBI 1log32.3 10 (6.2)

Where I = information capacity (bps)

B = bandwidth (Hz)

N

S= signal-to-noise ratio (unitless)

6.2.2 M-ary Encoding

M-ary is a term derived from word binary. M simply represents a digit that corresponds to

the number of conditions, levels or combinations possible for a given number of binary

variables.

• For example, a digital signal with four possible conditions (voltage levels,

frequencies, phases and so on) is an M-ary system where M = 4. If there are eight

possible conditions, M = 8 and so forth.

• The number of bits necessary to produce a given number of conditions is

expressed mathematically as

MN 2log= (6.3)

Where N = number of bits necessary

M = number of conditions or levels possible with N bits

• Equation (6.3) can be rearranged to express the number of conditions possible

with N bits

MN

=2 (6.4)

• For example, with one bit, only 2 conditions are possible. With two bits, 4 conditions are possible, with three bits, 8 conditions are possible, and so on.

6.2.3 Baud

Baud is a term often misunderstood and commonly confused with bit rate. Bit rate refers to the rate of change of a digital information signal, which is usually binary. Baud is also

a rate of change; however,



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Baud refers to the rate of change of a signal on the transmission medium after encoding

and modulation have occurred.

• I.e. baud is a unit of transmission rate, modulation rate or symbol rate and

therefore the terms symbols per second and baud are often used interchangeably.

• Mathematically, baud is expressed as

baud st

1= (6.5)

Where baud = symbol rate (symbol per second)

st = time of one signaling element or symbol (seconds)

Comparison between baud and bit rate can be further explained as the following. Binary signals are generally encoded and transmitted one bit at a time in the form of discrete

voltage levels representing logic 1 (high) or 0 (low). A baud is also transmitted one at a time; however, a baud may represent more than one information bit.

• I.e. the baud of a data communication system may be considerably less than the bit rate.

• In binary encoding systems, baud and bit rate (bps) are equal.

• In higher-level encoding systems, bit rate is always greater than baud.

Worked Example

Assume we wanted to transmit the decimal number 201. This can be represented in binary as 11001001.

Using binary (2-level) encoding system, these bits are transmitted serially as a sequence of equal-time-interval pulses that are either 1 or 0.

• If each bit interval is 1 ms, then the bit rate is 1000 bps (1/1ms).

• The baud rate is also 1000 bps or 1000 baud (1000 symbols per second). Now, let a 4-level encoding system represents 2 bits of data as different voltage levels.

Since there are 4 possible combinations of 2 bits, we will have 4 different voltage levels. For example,

00 – 0V 01 – 1V 10 – 2V 11 – 3V

• With this system, 11001001 would be divided into groups of 11/00/10/01. Therefore, the transmitted signal would be voltage levels of 3V, 0V, 2V and 1V

respectively.

• If each voltage level occurs at 1 ms interval, the baud rate is still 1000 baud because there is only one symbol per time interval. (I.e. 1000 symbols per second)



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• The bit rate now is 2000 bps since each symbol represents 2 bits (1000 x 2).

I.e. we have doubled the bit rate while keeping the baud rate constant. In addition, the transmission time is also shortened. It takes 8 ms to transmit 8-bit binary word using

binary system, but it only takes 4 ms to transmit the word using 4-level encoding system.

6.2.4 Minimum Bandwidth

According to H. Nyquist, binary digital signals can be propagated through an ideal noiseless transmission medium at a rate equal to two times the bandwidth of the medium.

The minimum theoretical bandwidth necessary to propagate a signal is called the

minimum Nyquist bandwidth or sometimes the minimum Nyquist frequency.

• Mathematical representation: Bfb 2= (6.6)

Where bf = Bit rate / Channel capacity (bps)

B = minimum Nyquist bandwidth (Hz)

• The relationship between bandwidth and bit rate also applies to the opposite situation. For a given bandwidth (B), the highest theoretical bit rate is 2B.

• However, if more than two levels are used for signaling, more than one bit may be transmitted at a time, and it is possible to propagate a bit rate that exceeds 2B.

• Using multi-level signaling, equation (6.6) becomes

MBfb 2log2= (6.7)

Where bf = Bit rate / Channel capacity (bps)

B = minimum Nyquist bandwidth (Hz) M = number of conditions or level

Worked example

Using previous worked example parameters, the minimum bandwidth required to

transmit the signal on binary encoding system can be calculated as

5002/10002/2 ===⇒= bb fBBf Hz

For the 4-level encoding system, the minimum bandwidth is similar.

500)2(2

2000

4log2

2000

log2log2

22

2 ====⇒=M

fBMBf b

b Hz

I.e. for a same bandwidth, we can propagate a higher bit rate using multi-level system.



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Equation (6.7) can be further simplified to solve for the minimum bandwidth necessary to

pass M-ary digitally modulated carrier:

M

fB b

2log= (6.8)

• Substituting Equation (6.3) into Equation (6.8)

N

fB b= (6.9)

Where N = number of bits encoded into each signaling element

In addition to that, since baud is the encoded rate of change, it also equals the bit rate

divided by the number of bits encoded into one signaling element. Therefore

N

fbaud b= (6.10)

• I.e. the baud and the ideal minimum Nyquist bandwidth have the same value and

are equal to the bit rate divided by the number of bits encoded. This is true for all

forms of digital modulation except frequency-shift keying.

6.3 Digital Modulation

Digital modulation is the transmittal of digitally modulated analog signals (carriers)

between two or more points in a communication system. Digital modulation is sometimes

called digital radio because digitally modulated signals can be propagated through

Earth’s atmosphere and used in wireless communication systems.

Figure 6.1 shows a simplified block diagram for a digital modulation system.

• Encoder performs level conversion and then encodes the incoming data into

groups of bits that modulate an analog carrier inside modulator.

• The modulated carrier is filtered, amplified and then transmitted through

transmission medium to the receiver.

• The transmission medium can be metallic cable, optical fiber cable, Earth’s

atmosphere or combination of two or more types of transmission systems.

• The received signal is filtered, amplified and then applied to the demodulator and

decoder circuits, which extracts the original source information from the

modulated carrier.

• The clock and carrier recovery circuits recover the analog carrier and digital

timing (clock) signals from the incoming modulated wave for demodulation

purpose.



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Figure 6.1: Simplified block diagram of digital modulation system

In general, there are three basic digital modulation techniques, namely: Amplitude Shift

keying (ASK), Frequency Shift Keying (FSK) and Phase Shift Keying (PSK). Figure 6.2

shows the output waveform for these three digital modulation techniques.

Figure 6.2: ASK, FSK and PSK modulation scheme



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• In ASK, the modulator puts out a burst of carrier for every logic 1, and no signal

for every logic 0.

• In FSK, for logic 1 a higher frequency carrier burst is transmitted and for logic 0 a

lower frequency carrier burst is transmitted, or vice versa.

• In PSK, logic 1 is transmitted as a burst of carrier with zero initial phase while

logic 0 is transmitted as a burst of carrier with 1800 initial phase.

6.3.1 Amplitude Shift Keying (ASK)

The simplest digital modulation technique is ASK, where a binary information signal

directly modulates the amplitude of an analog carrier. ASK can be represented

mathematically as

+= )cos(

2)](1[)()( t

Atvtv cmask ω (6.11)

Where )()( tv ask = ASK wave, )(tvm

= digital information (modulating) signal

2

A = unmodulated carrier amplitude,

c

ω = analog carrier radian frequency

• The modulating signal in Equation (6.11) is a normalized binary waveform, where

+1V = logic 1 and -1V = logic 0.

• For logic 1 input,

)cos()cos(2

]11[)(1)( )( tAtA

tvtv ccaskm ωω =

+=⇒+=


0)cos(2

]11[)(1)( )( =

−=⇒−= t

Atvtv caskm ω

• I.e., the ASK signal is either )cos( tAc

ω (ON) or 0 (OFF), which is why ASK is

also called on-off keying (OOK).

Figure 6.3 shows an example of ASK waveform.

Figure 6.3: ASK waveform



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• For every change in the input binary data, there is one change in the ASK

waveform and the time of one bit (tb) equals the time of one analog signaling

element (ts).

• Since the bit time is the reciprocal of the bit rate and the time of one signaling

element is the reciprocal of the baud, therefore, the bit rate in ASK modulation

technique is equal to the baud.

• With ASK, the bit rate is also equal to the minimum Nyquist bandwidth B (by

setting N = 1 into Equation (6.9) and Equation (6.10))

b

bb ff

N

fB ===

1 and

b

bb ff

N

fbaud ===

1

6.3.2 Frequency Shift Keying (FSK)

FSK is a form of constant-amplitude angle modulation similar to standard frequency

modulation (FM) except that the modulating signal is a binary signal that varies between

two discrete voltage levels rather than a continuously changing analog waveform. FSK is

also known as binary FSK (BFSK).

• Mathematical expression for FSK

[ ][ ]tftvfVtv mccfsk ∆+= )(2cos)()( π (6.12)

Where )()( tv fsk = FSK wave

)(tvm

= binary input (modulating) signal

c

V = peak analog carrier amplitude

c

f = analog carrier centre frequency

f∆ = peak change (shift) in analog carrier frequency

• The modulating signal in Equation (6.12) is also a normalized binary waveform,

where +1V = logic 1 and -1V = logic 0.


( )[ ]tffVtvtv ccfskm ∆+=⇒+= π2cos)(1)( )(


( )[ ]tffVtvtv ccfskm ∆−=⇒−= π2cos)(1)( )(

With binary FSK, the carrier center frequency is shifted up and down in the frequency

domain by the binary input signal and the direction of the shift is determined by the

polarity as shown in Figure 6.4.



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Figure 6.4: FSK in the frequency domain

• As the binary input changes from logic 0 to logic 1 and vice versa, the output

frequency shifts between two frequencies: a mark or logic 1 frequency (fm) and a

space or logic 0 frequency (fs).

• The mark and space frequencies are separated from the carrier centre frequency

by the peak frequency deviation f∆ .

• Frequency deviation can be expressed mathematically as

2

smff

f−

=∆ (6.13)

Figure 6.5 shows an example of FSK waveform in time domain.

Figure 6.5: FSK waveform

• Based on Figure 6.5, the time of one bit (tb) is the same as the time of an FSK

signaling element (ts). I.e. the FSK bit rate is equal to the baud of FSK.

• Again by setting N = 1 in Equation (6.10),

b

bb ff

N

fbaud ===

1

fs fm fc

Logic 1

Logic 0

+∆f -∆f



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FSK is the exception to the rule for digital modulation, as the minimum Nyquist

bandwidth B is not determined using Equation (6.9).

• The minimum Nyquist bandwidth for FSK is given as

bmsbmbs fffffffB 2)()( +−=−−−=

Since fff ms ∆=− 2 as in Equation (6.13),

)(2b

ffB +∆= (6.14)

6.3.3 Phase Shift Keying (PSK)

PSK is another form of angle-modulated, constant-amplitude digital modulation. PSK is

an M-ary digital modulation scheme similar to conventional phase modulation except

with PSK the input is a binary digital signal and there are limited numbers of output

phase possible. The number of output phases is defined by M as described in Equation

(6.4) and determined by the number of bits N.

The simplest form of PSK is binary PSK (BPSK), where N = 1 and M = 2. Therefore,

with BPSK, two phases are possible for the carrier.

• One phase represents logic 1 and the other phase represents logic 0.

• As the input digital / binary signal changes state, the phase of the output carrier

shifts between two angles that are separated by 1800.

Figure 6.6 shows a simplified block diagram of BPSK transmitter

Figure 6.6: BPSK transmitter

• If +1 V is assigned to input logic 1 and -1 V is assigned to input logic 0, the

carrier )sin( tc

ω is multiplied by either +1 or -1.

Balanced

modulator

Band pass

filter

Level

converter

(unipolar to

bipolar)

Reference carrier

oscillator

Modulated

PSK output

Binary data

(modulating)

Buffer

sin (ωct)



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• For logic 1, the output BPSK signal is )sin()()( ttv cpsk ω= while for logic 0, the

output BPSK signal is )sin()()( ttv cpsk ω−= .

• I.e. logic 1 output represents a signal that is in phase with the reference oscillator

and logic 0 output represents a signal that is 1800

out of phase with reference

oscillator.

Figure 6.7 shows an example of BPSK waveform.

Figure 6.7: BPSK waveform

• As binary input shifts between logic 1 and logic 0 and vice versa, the phase of the

BPSK waveform shifts between 00 to 180

0, respectively.

• For simplicity, only one cycle of the analog carrier in shown in each signaling

element, although there may be anywhere between a fraction of a cycle to several

thousand cycle, depending on the relationship between the input bit rate and the

analog carrier frequency.

• Note that the time of one BPSK signaling element (ts) is equal to the time of one

input bit (tb), which indicates that the bit rate equals the baud.

• As in ASK, the minimum Nyquist bandwidth B for FSK is given as

b

b ff

B ==2

2

6.4 Digital Transmission

Digital transmission is the transmittal of digital signals between two or more points in a

communication system. The signals can be binary or any other form of discrete-level

digital pulses. The original source information may be in digital form or it could be

analog signals that have been converted to digital pulses prior to transmission.

With digital transmission systems, a physical facility, such as a pair or wires, coaxial

cable or an optical fiber cable, is required to interconnect the various points within the

system. Note that digital pulses cannot be propagated through a wireless transmission

system, such as Earth’s atmosphere or free space.



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6.4.1 Pulse Modulation

Pulse modulation is a process of sampling analog information signals and then converting

those samples into discrete pulses and transporting the pulses from a source to a

destination over a physical transmission medium. The four predominant methods of pulse

modulation are Pulse Width Modulation (PWM), Pulse Position Modulation (PPM),

Pulse Amplitude Modulation (PAM) and Pulse Code Modulation (PCM).

• In PWM, the width of constant-amplitude pulse is varied proportional to the

amplitude of the analog signal at the time the signal is sampled.

• In PPM, the position of a constant-width and constant-amplitude pulse is varied

according to the amplitude of the sample of the analog signal.

• In PAM, the amplitude of a constant-width pulse is varied proportional to the

amplitude of the sample of the analog signal.

• In PCM, the analog signal is sampled and then converted to a serial n-bit binary

code for transmission. Each code has the same number of bits and requires the

same length of time for transmission.

Figure 6.8 shows examples of PWM, PPM and PAM waveforms.

Figure 6.8: PWM, PPM and PAM waveforms

• For PWM, the maximum analog signal amplitude produces the widest pulse and

the minimum analog signal amplitude produces the narrowest pulse.

• For PPM, the higher the sample’s amplitude, the farther to the right the pulse is

positioned within the prescribed time slot. The highest amplitude sample produces

a pulse to the far right while the lowest amplitude sample produces a pulse to the

far left.

• For PAM, the amplitude of a pulse coincides with the amplitude of the analog

signal.



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PAM is used as an intermediate form of modulation with PSK and PCM, although it is

seldom used by itself. PWM and PPM are used in special-purpose communication

systems mainly for the military but are seldom used for commercial digital transmission

systems. PCM is by far the most prevalent form of pulse modulation and will be

discussed in more detail in subsequent section of this chapter.

6.4.2 Pulse Code Modulation (PCM)

Figure 6.9 shows simplified block diagram of a single-channel, simplex PCM system.

Figure 6.9: PCM system

• Band pass filter limits the frequency of analog signal to standard voice-band

frequency range.

• Sample and hold circuit samples the analog signal and converts those samples to a

multilevel PAM signal.

• Analog-to-digital converter converts multilevel PAM samples to parallel PCM

codes.

• Parallel-to-serial converter converts parallel PCM codes to serial binary data.

• Repeaters are placed at prescribed distances to regenerate the data.

Band pass

filter

Sample and

hold

Analog input

signal

Analog to

digital

converter

Sample pulse

Conversion

clock

Parallel to

serial

converter

Line speed

clock

Regenerative

repeater

PAM signal Parallel data

Regenerative

repeater

Digital to analog

converter

Serial to parallel

converter

Parallel data

Conversion

clock

Line speed

clock

Hold circuit Low pass

filter

Analog output

signal

PAM signal

Serial PCM

code

Serial PCM

code

Serial PCM

code



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• Serial-to-parallel converter converts serial binary data to parallel PCM codes.

• Digital-to-analog converter converts parallel PCM codes to multilevel PAM

signals.

• Hold circuit and low pass filter converts PAM signals back to its original form.

6.4.2.1 Sampling and sampling rate

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 pulses

that can more easily be converted to binary PCM code.

The Nyquist sampling theorem establishes the minimum sampling rate that can be used

for a given PCM system. The theorem states that,

The original analog input signal can be reconstructed at the receiver with minimal

distortion if the sampling rate in the pulse modulation system is equal to or greater than

twice the maximum analog input frequency.

• Mathematical representation:

(max)2 ms ff ≥ (6.15)

Where fs = sampling rate / sampling frequency

fm(max) = maximum analog input frequency

• I.e. the minimum sampling rate is equal to twice the highest analog input

frequency.

6.4.2.2 Quantization

Quantization is a process of converting an infinite number of possibilities to a finite

number of conditions. In relations to this chapter, once the analog signal is sampled,

quantization is a process of assigning those samples to pre-determined discrete

quantization levels.

• The number of quantization levels L depends on the number of bits per sample

used to code the analog signal.

n

L 2= (6.16)

• The magnitude difference between adjacent levels is called the quantization

interval or quantum or resolution.

• The resolution is equal to the voltage of the minimum step size, which in turn is

equal to the voltage of the least significant bit of the PCM code. It can be

represented mathematically as



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1

minmax

−

−=∆

L

VVV (6.17)

Where V∆ = resolution,

maxV = maximum analog input signal

minV = minimum analog input signal

In most cases, the likelihood of a sample voltage is exactly the same as one of the

quantization level values is remote. Therefore, each sample voltage is rounded off

(quantized) to the closest available level. This process leads to an error called

quantization error or quantization noise.

• It is the distortion introduced during quantization process when the analog sample

voltage is not exact value of the quantized level.


)]([)]([ tqtxQe

−= (6.18)

Where e

Q = quantization error / quantization noise

)]([ tx = magnitude of analog sample voltage

)]([ tq = magnitude of the closest quantized level

• Maximum quantization error is given by 2

(max)

VQ

e

∆±= (6.19)

• Quantization error can be reduced by increasing the number of quantization

levels, but this will increase the bandwidth required to transmit the signal.

• Signal-to-quantization noise ratio (SQR):

eQ

VSQR = (6.20)

In decibel, q

v

q

vSQR log208.10

12/log10

2

2

+=

= (6.21)

Where v = rms signal voltage

q = quantization interval

6.4.2.3 Encoding

This is the process where each quantized sample is digitally encoded into n-bits codes,

where n maybe any positive integer greater than 1.

Ln 2log= (6.22)



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• The codes currently used for PCM are sign-magnitude codes, where the most

significant bit (MSB) is the sign bit and the remaining bits are used for

magnitude.

• Table 6.1 shows an n-bit PCM code where n equals 3.

Table 6.1: 3-bit PCM code

Sign bit Magnitude / Value bit

0 00

0 01

0 10

0 11

1 00

1 01

1 10

1 11

MSB is used to represent the sign of sample where logic 1 represent positive

value sample while logic 0 represent negative value sample.

Figure 6.10 shows all parameters related to 3-bit PCM system.

Figure 6.10: Quantization level, resolution, quantization error, sign bit, and magnitude bit



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Figure 6.11 shows an analog waveform, sampling pulse, the corresponding sampled

signal (PAM), quantized signal and PCM code for each sample.

Figure 6.11: (a) Input signal, (b) sampling pulse, (c) PAM signal, (d) quantized signal and

(e) PCM code



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6.4.2.4 Dynamic Range

The number of PCM bits transmitted per sample is determined by several variables,

which includes maximum allowable input amplitude, resolution and dynamic range.

Dynamic range (DR) is the ratio of the largest possible magnitude to the smallest

possible magnitude that can be decoded by the digital-to-analog converter (DAC) in the

receiver.


V

V

V

VDR

∆== max

min

max (6.23)

Where maxV = maximum voltage that can be decoded by DAC

VV ∆=min = resolution

• The relationship between DR and the number of bits in a PCM code:

DRn

≥−12 (6.24)

For a minimum number of bits, DRn =−12 (6.25)

Where n = number of bits in a PCM code, excluding sign bit

• Rearranging Equation (6.25), we can solve for n by taking logs:

)1log(2log)1log(2log +=⇒+= DRnDRn

2log

)1log( +=

DRn

• DR can also be expressed in decibels:

( )12log20log20)(min

max −=

=

n

V

VdbDR (6.26)

6.4.2.5 Coding Efficiency

Coding efficiency is a numerical indication of how efficiently a PCM code is utilized. It is

a ratio of the minimum number of bits required to achieve a certain dynamic range to the

actual number of PCM bits used. I.e.:

100)(

)(×=

bitsignincludingbitsofnumberActual

bitsignincludingbitsofnumberMinefficiencyCoding (6.27)



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6.4.3 Companding

Companding is a process of compressing and then expanding. With companded systems,

the higher-amplitude analog signals are compressed (amplified less than the lower-

amplitude signals) prior to transmission and then expanded (amplified more than the

lower-amplitude signals) in the receiver.

• Companding is a means of improving the dynamic range of a communication

system.

• There are two methods of analog companding for PCM system: µ-Law

companding and A-Law companding.

6.4.3.1 µ-Law companding

• Used in the US and Japan.

• The compression characteristics for µ-Law:

)1ln(

)/1ln( maxmax

µ

µ

+

+=

VVVV in

out (6.28)

Where out

V = compressed output amplitude

maxV = maximum uncompressed analog input amplitude

in

V = amplitude of the input signal at a particular instant of time

µ = parameter used to define the amount of compression

Figure 6.12 shows the compression curve for several values of µ. Note that the higher the

µ, the more compression.

Figure 6.12: µ-Law compression characteristics



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6.4.3.2 A-Law companding

• Used in Europe and other parts of the world.

• The compression characteristics for A-Law:

A

VAVVV in

outln1

/ max

max+

= for AV

Vin 1

0max

≤≤ (6.28a)

A

VAVVV in

outln1

)/ln(1 max

max+

+= for 1

1

max

≤≤V

V

A

in (6.28b)

Figure 6.13 shows the compression curves for several values of A.

Figure 6.13: A-Law compression characteristics

For an intended dynamic range, A-Law companding has a slightly flatter SQR than µ-

Law. However, A-Law companding is inferior to µ-Law in terms of small-signal quality.

6.4.4 Delta Modulation PCM

With conventional PCM, each code is a binary representation of both sign and the

magnitude of a particular sample. Therefore, multiple-bit codes are required to represent

the many values that the sample can be. With delta modulation, rather than transmit a

coded representation of the sample, only a single bit is transmitted, which simply

indicates whether that sample is larger of smaller than the previous sample.



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• If the current sample is smaller than the previous sample, logic 0 is transmitted. If

the current sample is larger than the previous sample, logic 1 is transmitted.

6.4.4.1 Delta Modulation Transmitter

Figure 6.14 shows a block diagram of a delta modulation transmitter.

Figure 6.14: Delta modulation transmitter

• The input analog is sampled and converted to a PAM signal, which is compared

to the output of the DAC.

• The output of the DAC is a voltage equal to the regenerated magnitude of the

previous sample (stored in the up-dowm counter as a binary number)

• The up-down counter is incremented or decremented depending on whether the

previous sample is larger or smaller than the current sample. It is clocked at a rate

equal to the sample rate (i.e. updated after each comparison)

Figure 6.15 shows the ideal operation of a delta modulation encoder.

Figure 6.15: Ideal operation of a delta modulation encoder



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• Initial conditon: Up-down counter is zeroed, DAC ouput = 0V.

• When the first sample is taken and converted to PAM signal, it is compared to

zero volts. The output of the comparator is logic 1 (current sample is larger in

amplitude than the previous sample).

• Next clock pulse, the counter is updated (incremented to a count of 1). The DAC

now outputs a voltage equal to the magnitude of minimum step size / resolution.

The second sample is now compared to the new DAC output, and so on.

Based on Figure 6.15, the up-down counter follows the input analog sample

(incremented) until the output of the DAC exceeds the analog sample amplitude; then it

will begin counting down (decremented) until the output of the DAC drops below the

sample amplitude.

• Each time the up-down counter is incremented, logic 1 is transmitted, and each

time the up-down counter is decremented, logic 0 is transmitted.

6.4.4.2 Delta Modulation Receiver

Figure 6.16 shows the block diagram of a delta modulation receiver.

Figure 6.16: Delta modulation receiver

• The receiver almost identical to the transmitter except for the comparator.

• As the logics 1 and 0 are received, the counter is incremented or decremented

accordingly. Consequently, the output of the DAC in the reciever is identical to

the output of the DAC in the transmitter (Figure 6.16).

With delta modulation, each sample requires the transmission of only one bit, therefore

the bit rates associated with delta modulation are lower than conventional PCM systems.

However, there are two problems associated with delta modulation that do not occur with

conventional PCM: slope overload and granular noise.



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Slope overload:

Figure 6.17: Slope overload distortion

• Occurs when the analog input signal changes at a faster rate than the DAC can

maintain.

• The slope of the analog signal is greater than the delta modulator can maintain.

• Solutions: increase the clock frequency or increase the magnitude of the minimum

step size (resolution).

Granular noise:

Figure 6.18 contrasts the original and reconstructed signals associated with delta

modulation system.

Figure 6.18: Granular noise

• When the original signal has a relatively constant amplitude, the reconstructed

signal has variations that were not present in the original signal. This is called

granular noise.

• It can be reduced by decreasing the step size (resolution)

Note that to reduce the granular noise, a small resolution is needed while to reduce the

slope overload, a large resolution is required. I.e. a compromise is necessary.

• Granular noise is more prevelant in analog signals that have gradual slope and

whose amplitudes vary only a small amount.

• Slope overload is more prevalent in analog signals that have steep slopes or

whose amplitudes vary rapidly.

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Chapter 6: Introduction to Digital Communicationmyweb.utem.edu.my/myweb/noorazwan/Chapter_6.pdf · high-frequency analog carriers are modulated by relatively low ... forms of digital