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□Basic scheme of PCM system□Quantization□Quantization Error□Companding□Block diagram & function of TDM-PCM
communication system
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Basic scheme of PCM system
□The most common technique for using digital signals to encode analog data is PCM.
□Example: To transfer analog voice signals off a local loop to digital end office within the phone system, one uses a codec.
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Cont’d...
□Because voice data limited to frequencies below 4000 Hz, a codec makes 8000 samples/sec. (i.e., 125 microsecond/sample).
□If a signal is sampled at regular intervals at a rate higher than twice the highest signal frequency, the samples contain all the information of the original signal.
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PCM Block Diagram
• Most common form of analog to digital modulation• Four step process
1. Signal is sampled using PAM (Sample)
2. Integer values assigned to signal (PAM)
3. Values converted to binary (Quantized)
4. Signal is digitally encoded for transmission (Encoded)
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4 Steps Process
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Cont’d…□ Analog signal is sampled.□ Converted to discrete-time continuous-amplitude signal (Pulse Amplitude Modulation)
□ Pulses are quantized and assigned a digital value.□ A 7-bit sample allows 128 quantizing levels.
□ PCM uses non-linear encoding, i.e., amplitude spacing of levels is non-linear□ There is a greater number of quantizing steps for low amplitude□ This reduces overall signal distortion.
□ This introduces quantizing error (or noise).□ PCM pulses are then encoded into a digital bit stream.□ 8000 samples/sec x 7 bits/sample = 56 Kbps for a single voice
channel.
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PCM Example
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Quantization
□ A process of converting an infinite number of possibilities to a finite number of conditions (rounding off the amplitudes of flat-top samples to a manageable number of levels).
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Cont’d...
Analog input signal
Sample pulse
PAM signal
PCM code
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The quantization interval @ quantum = the magnitude difference between adjacent steps.
The resolution = the magnitude of a quantum = the voltage of the minimum step size.
The quantization error = the quantization noise = ½ quantum = (orig. sample voltage – quantize
level)
PCM code = (sample voltage/resolution)
Cont’d…
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□ A difference between the exact value of the analog signal & the nearest quantization level.
QUANTIZATION ERROR
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Types of Quantization
Midtread Midrise
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Types of Quantizer1. Uniform type : The levels of the quantized amplitude are uniformly spaced. 2. Non-uniform type : The levels are not uniform.
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Dynamic Range (DR)
□ Largest possible magnitude/smallest possible magnitude.
□ Where □ DR = absolute value of dynamic range□ Vmax = the maximum voltage magnitude□ Vmin = the quantum value (resolution)□ n = number of bits in the PCM code
resolution
V
V
VDR max
min
max
12 nDR
)log(20)( DRdBDR
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Example 1
1. Calculate the dynamic range for a linear PCM system using 16-bit quantizing.
2. Calculate the number of bits in PCM code if the DR = 192.6 dB
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Coding Efficiency
□A numerical indication of how efficiently a PCM code is utilized.
□The ratio of the minimum number of bits required to achieve a certain dynamic range to the actual number of PCM bits used.
Coding Efficiency = Minimum number of bits x 100
Actual number of bits
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Signal to Quantization Noise Ratio (SQR)
□ The worst-case voltage SQR
□ SQR for a maximum input signal
□ The signal power-to-quantizing noise power ratio
eQ
resolutionSQR (min)
eQ
VSQR max
(max)
12
2
12
)(
22
2
log10)(
log10
power noiseon quantizati average
power signal averagelog10
Rv
dB
v
R
SQR
R =resistance (ohm)
v = rms signal voltage
q = quantization interval
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Example 2
1. Calculate the SQR (dB) if the input signal = 2 Vrms and the quantization noise magnitudes = 0.02 V.
2. Determine the voltage of the input signals if the SQR = 36.82 dB and q =0.2 V.
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Effect of Non-Linear Coding
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Nonlinear Encoding
□ Quantization levels not evenly spaced
□ Reduces overall signal distortion
□ Can also be done by companding
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Companding
• The process of compressing and then expanding.
• The higher amplitude analog signals are compressed
prior to transmission and then expanded in receiver.
• Improving the DR of a communication system.
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Companding Functions
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Method of Companding□ For the compression, two laws are adopted: the -law
in US and Japan and the A-law in Europe.
□ -law□
□ A-law
□ The typical values used in practice are: =255 and A=87.6.
□ After quantization the different quantized levels have to be represented in a form suitable for transmission. This is done via an encoding process.
)1ln(
)1ln(maxmax
VV
out
inVV
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ln1
)ln(1
10
ln1
max
max
max
out
inVV
out
inVV
out
V
V
AA
AAV
V
A
AV
Vin
in
Vmax= Max uncompressed analog input voltage
Vin= amplitude of the input signal at a particular of instant time
Vout= compressed output amplitude
A, = parameter define the amount of compression
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Example 3
□A companding system with µ = 255 used to compand from 0V to 15 V sinusoid signal. Draw the characteristic of the typical system.
□Draw an 8 level non-uniform quantizer characteristic that corresponds to the mentioned µ.
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Cont’d...
μ-law A-law
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PCM Line Speed
□ The data rate at which serial PCM bits are clocked out of the PCM encoder onto the transmission line.
□ Where□Line speed = the transmission rate in bits per
second
□Sample/second = sample rate, fs
□Bits/sample = no of bits in the compressed PCM code
sample
bitsX
second
samples speed line
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Example 4
□For a single PCM system with a sample rate fs = 6000 samples per second and a 7 bits compressed PCM code, calculate the line speed.
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Virtues & Limitation of PCM
The most important advantages of PCM are:□Robustness to channel noise and
interference.□Efficient regeneration of the coded
signal along the channel path.
□Efficient exchange between BT and SNR.
□Uniform format for different kind of base-band signals.
□Flexible TDM.
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Cont’d…□Secure communication through the use of
special modulation schemes of encryption.□These advantages are obtained at the cost of
more complexity and increased BT.
□With cost-effective implementations, the cost issue no longer a problem of concern.
□With the availability of wide-band communication channels and the use of sophisticated data compression techniques, the large bandwidth is not a serious problem.
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□Information capacity, Bits & Bit Rate□Represents the number of independent
symbols that can be carried through a system in a given unit of time.
□Basic digital symbol is the binary digit or bit.
□Express the information capacity as a bit rate.
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Hartley’s Law
tBI Where
I = information capacity (bps)
B = bandwidth (Hz)
t = transmission time (s)
From the equation, Information capacity is a linear function of bandwidth and transmission time and directly proportional to both.
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Shannon’s Formula
)1(log32.3)1(log 102 NS
NS BIorBI
Where
I = information capacity (bps)
B = bandwidth (Hz)
= signal to noise power ratio (unitless)
The higher S/N the better the performance and the higher the information capacity
NS
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Example 2
By using the Shannon’s Formula, calculate the information capacity if S/N = 30 dB and B = 2.7 kHz.
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Nyquist Sampling Rate
□fs is equal or greater than 2fm
fs >= 2fm
fs = minimum Nyquist sample rate (Hz)fm = maximum analog input frequency (Hz)
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Example 3
Determine the Nyquist sample rate for a maximum analog input frequency 7.5 kHz.
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M-ary Encoding
□ It is often advantageous to encode at a level higher than binary where there are more then two conditions possible.
□ The number of bits necessary to produce a given number of conditions is expressed mathematically as
MN 2log
Where N = number of bits necessary
M = number of conditions, level or combinations possible with N bits.
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Cont’d…
□Each symbol represents n bits, and has M signal states, where M = 2N.
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Example 4
Find the number of voltage levels which can represent an analog signal with
a. 8 bits per sample b. 12 bits per sample
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Baud & Minimum BW
□ Baud refers to the rate of change of a signal on the transmission medium after encoding and modulation have occurred.
Where
baud = symbol rate (symbol per second)
ts = time of one signaling element @ symbol (seconds)
stbaud
1
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Cont’d…
□ Minimum Bandwidth □ Using multilevel signaling, the Nyquist formulation for
channel capacity
MBfb 2log2
Where fb= channel capacity (bps)
B = minimum Nyquist bandwidth (Hz)
M = number of discrete signal or voltage levels
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Cont’d…
baudN
f
M
fB bb
2log
Where N is the number of bits encoded into each signaling element.
For B necessary to pass M-ary digitally modulated carriers
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□ Converting standard logic level to a form more suitable to telephone line transmission.
□ The line codes properties:1. Transmission BW should be small as
possible2. Efficiency should be as high as possible3. Error detection & correction capability4. Transparency (Encoded signal is
received faithfully)
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Cont’d...
□Six factors must be considered when selecting a line encoding format;
1.transmission voltage & DC component
2.Duty cycle3.Bandwidth consideration4.Clock and framing bit recovery5.Error detection6.Ease of detection and decoding
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Why Digital Signaling?
□Low cost digital circuits
□The flexibility of the digital approach (because digital data from digital sources may be merged with digitized data derived from analog sources to provide general purpose communication system)
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Digital Modulation□ Using Digital Signals to Transmit Digital Data
□ Bits must be changed to digital signal for transmission□ Unipolar encoding
□Positive or negative pulse used for zero or one□ Polar encoding
□Uses two voltage levels (+ and - ) for zero or one□ Bipolar encoding
□+, -, and zero voltage levels are used
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Non-Return to Zero-Level (NRZ-L)
□ Two different voltages for 0 and 1 bits.□ Voltage constant during bit interval.
□ no transition, no return to zero voltage□ More often, negative voltage for one value and
positive for the other.
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Non-Return to Zero Inverted (NRZ-I)
□ Nonreturn to zero inverted on ones□ Constant voltage pulse for duration of bit□ Data encoded as presence or absence of signal
transition at beginning of bit time□ Transition (low to high or high to low) denotes a
binary 1□ No transition denotes binary 0□ An example of differential encoding
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Multilevel Binary(Bipolar-AMI)
• zero represented by no line signal• one represented by positive or negative pulse• one pulses alternate in polarity• No loss of sync if a long string of ones (zeros still
a problem)• No net dc component• Lower bandwidth• Easy error detection
0 1 0 0 1 1 0 0 0 1 1
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Pseudoternary
□ One represented by absence of line signal□ Zero represented by alternating positive and
negative□ No advantage or disadvantage over bipolar-AMI
0 1 0 0 1 1 0 0 0 1 1
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Manchester□ There is always a mid-bit transition {which is
used as a clocking mechanism}.
□ The direction of the mid-bit transition represents the digital data.
□ 1 low-to-high transition
□ 0 high-to-low transition
□ Consequently, there may be a second transition at the beginning of the bit interval.
□ Used in 802.3 baseband coaxial cable and CSMA/CD twisted pair.
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Differential Manchester□ mid-bit transition is ONLY for clocking.
□ 1 absence of transition at the beginning of the bit interval
□ 0 presence of transition at the beginning of the bit interval
□ Differential Manchester is both differential and bi-phase.
[Note – the coding is the opposite convention from NRZI.]
□ Used in 802.5 (token ring) with twisted pair.
□ * Modulation rate for Manchester and Differential Manchester is twice the data rate inefficient encoding for long-distance applications.
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Example 5
□Sketch the data wave form for a bit stream 11010 using□NRZL□Bipolar AMI□Pseudoternary
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Forms of Digital Modulation
)2sin()( ftVtv
•If the amplitude, V of the carrier is varied proportional to the information signal, a digital modulated signal is called Amplitude Shift Keying (ASK)
•If the frequency, f of the carrier is varied proportional to the information signal, a digital modulated signal is called Frequency Shift Keying (FSK)
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Cont’d…
□ If the phase, θ of the carrier is varied proportional to the information signal, a digital modulated signal is called Phase Shift Keying (PSK)
□ If both the amplitude and the phase, θ of the carrier are varied proportional to the information signal, a digital modulated signal is called Quadrature Amplitude Modulation (QAM)
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Cont’d...
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Block Diagram
Simplified block diagram of a digital modulation system
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Cont’d…
□Precoder performs level conversion & encodes incoming data into group of bits that modulate an analog carrier.
□Modulated carrier filtered, amplified & transmitted through transmission medium to Rx.
□In Rx, the incoming signals filtered, amplified & applied to the demodulator and decoder circuits which extracts the original source information from modulated carrier.
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□Amplitude Shift Keying (ASK)□Frequency Shift Keying (FSK)□Phase Shift Keying (PSK)
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Amplitude Shift Keying (ASK)
□ A binary information signal directly modulates the amplitude of an analog carrier.
□ Sometimes called Digital Amplitude Modulation (DAM)
)cos()](1[)( 2 ttvtv cA
mask
Where vask (t) = amplitude shift keying wave
vm(t) = digital information signal (volt)
A/2 = unmodulated carrier amplitude (volt)
ωc = analog carrier radian frequency (rad/s)
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Cont’d...
1)(,'0'logic0
1)(,'1'logic)cos()(
tvfor
tvfortAtv
m
mcask
Digital Amplitude Modulation
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Frequency Shift Keying (FSK)
□ Called as Binary Frequency Shift Keying (BFSK)□ The phase shift in carrier frequency (∆f) is proportional
to the amplitude of the binary input signal (vm(t)) and the direction of the shift is determined by the polarity
tftvfVtv mccfsk ])([2cos)(
Where vfsk(t) = binary FSK waveform
Vc = peak anlog carrier amplitude (volt)
fc = analog carrier center frequency (Hz)
∆f = peak shift in analog carrier frequency (Hz)
vm(t) = binary input signal (volt)
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1)(,'0'logic][2cos
1)(,'1'logic][2cos)(
tvfortffV
tvfortffVtv
mcc
mccfsk
(Hz)frequency space &mark between difference absolute
(Hz)deviation frequency
,2
sm
sm
ff
f
where
fff
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)(22)()( bbmsbmbs fffffffffB
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Cont’d...
Binary Input Frequency Output
0 Space (fs)
1 Mark (fm)
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Phase Shift Keying (PSK)
□ Another form of angle-modulated, constant amplitude digital modulation.
□ Binary digital signal input & limited number of output phases possible.
□ M-ary digital modulation scheme with the number of output phases defined by M.
□ The simplest PSK is Binary Phase-Shift Keying (BPSK)□ N= 1, M=2□ Two phases possible for carrier with one phase for logic 1
and another phase for logic 0□ The output carrier shifts between two angles separated by
180°
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Cont’d...
a) Truth Table b) Phasor Diagram c) Constellation Diagram
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EXAMPLE ASK,FSK & PSK
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EXAMPLE ASK,FSK & PSK
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EXAMPLE ASK,FSK & PSK
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Exercise 4.1
For the digital message 1011 0100 1010, sketch the waveform for the following:
a. ASKb. FSK
c. PSK
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APPLICATIONS OF ASK,FSK & PSK
□ASK – It is used in multichannel telegraph systems. Simple ASK is no longer used in digital communication systems due to noise problems.
□FSK – are used mainly for low speed digital data transmissions.
□PSK_Owing to PSK's simplicity, it is widely used in existing technologies.
□Such as wireless LAN, bluetooth…
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END OF PART 2
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