Chapter 5. Pulse Modulation

From Analog to Digital

5.6 Pulse-Code Modulation

Pulse-Code Modulation

• Pulse-code modulation (PCM)– Most basic form of digital pulse modulation– A message signal is converted to discrete form in both

time and amplitude, and represented by a sequence of coded pulses

• The basic operation– Transmitter: sampling, quantization, encoding– Receiver: regeneration, decoding, reconstruction

2

5.6 Pulse-Code Modulation

Pulse-Code Modulation

3

5.6 Pulse-Code Modulation

Operations in the Transmitter

• Sampling– The incoming baseband signal is sampled with a train of

rectangular pulses at greater than Nyquist rate– Anti-alias (low-pass) filter

• Nonuniform quantization– In real sources such as voice, samples of small ampli-

tude appear frequently whereas large amplitude is rare.– Nonuniform quantizer is equivalent to compressor fol-

lowed by uniform quantizer.

4

5.6 Pulse-Code Modulation

Operations in the Transmitter

– –law compressor

– -law compressor

5

)24.5()1()1log(

mvd

md

)23.5()1log(

)1log(

mv

)25.5(

11

,log1

)log(1

10,

log1

m

AA

mA

Am

A

mA

v

)26.5(

11

,)log1(

10,

log1

m

AmA

Am

A

A

vd

md

5.6 Pulse-Code Modulation

Operations in the Transmitter

6

–law compressor

7

|m||v|

μ=0.01 μ=5 μ=20 μ=100

0.00 0.00 0.00 0.00 0.00 0.05 0.05 0.13 0.23 0.56 0.10 0.10 0.23 0.36 0.69 0.15 0.15 0.31 0.46 0.75 0.20 0.20 0.39 0.53 0.80 0.25 0.25 0.45 0.59 0.83 0.30 0.30 0.51 0.64 0.86 0.35 0.35 0.57 0.68 0.88 0.40 0.40 0.61 0.72 0.90 0.45 0.45 0.66 0.76 0.91 0.50 0.50 0.70 0.79 0.92 0.55 0.55 0.74 0.82 0.94 0.60 0.60 0.77 0.84 0.95 0.65 0.65 0.81 0.87 0.95 0.70 0.70 0.84 0.89 0.96 0.75 0.75 0.87 0.91 0.97 0.80 0.80 0.90 0.93 0.98 0.85 0.85 0.93 0.95 0.98 0.90 0.90 0.95 0.97 0.99 0.95 0.95 0.98 0.98 0.99 1.00 1.00 1.00 1.00 1.00

)23.5()1log(

)1log(

mv

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 Quantization

Input level

Output level

5.6 Pulse-Code Modulation

Operations in the Transmitter

• Encoding– To translate the discrete set of sample values to a more

appropriate form of signal– A binary code

• The maximum advantage over the effects of noise because a binary symbol withstands a relatively high level of noise.

• The binary code is easy to generate and regenerate

8

5.6 Pulse-Code Modulation

Operations in the Transmitter

9

5.6 Pulse-Code Modulation

Regeneration along the Transmission Path

• The ability to control the effects of distortion and noise produced by transmitting a PCM signal over a channel

• Ideally, except for delay, the regenerated signal is exactly the same as the information-bearing signal

• Equalizer: Compensate for the effects of amplitude and phase distortions produced by the transmission

• Timing circuitry: Renewed sampling of the equalized pulses

• Decision-making device

10

5.6 Pulse-Code Modulation

Operations in the Receiver

• Decoding– Regenerating a pulse whose amplitude is the linear sum of

all the pulses in the codeword

• Expander– A subsystem in the receiver with a characteristic comple-

mentary to the compressor– The combination of a compressor and an expander is

called a compander.

• Reconstruction– Recover the message signal by passing the expander out-

put through a low-pass reconstruction filter

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5.7 Delta Modulation

Basic Considerations

• Delta modulation (DM)– An incoming message signal is oversampled (at a rate

much higher than Nyquist rate).– The correlation between adjacent samples is introduced.– It permits the use of a simple quantization.– Quantization into two levels ()

•

where is an error signal

12

)27.5()()()( ssqss TnTmnTmnTe

)28.5()](sgn[)( ssq nTenTe

)29.5()()()( sqssqsq nTeTnTmnTm

5.7 Delta Modulation

Basic Considerations

13

5.7 Delta Modulation

System Details

• Comparator – Computes the difference between its two inputs

• Quantizer – Consists of a hard limiter with an input-output character-

istic that is a scaled version of the signum function

• Accumulator– Operates on the quantizer output so as to produce an

approximation to the message signal

14

(5.30) )(

)()()2(

)()()(

1

n

isq

sqssqssq

sqssqsq

iTe

nTeTnTeTnTm

nTeTnTmnTm

5.7 Delta Modulation

System Details

15

5.7 Delta Modulation

Quantization Errors

• Slope-overload distortion– Occurs when the step size is too small– The approximation signal falls behind the message sig-

nal

• Granular noise– Occurs when the step size is too large– The staircase approximation hunts around a flat seg-

ment.

16

5.7 Delta Modulation

Delta-Sigma Modulation

• Drawback of DM– An accumulative error in the demodulated signal

• Delta-sigma modulation (D-M)– Integrates the message signal prior to delta modulation

• Benefit of the integration– The low-frequency content of the input signal is pre-em-

phasized– Correlation between adjacent samples of the delta mod-

ulator input is increased – Design of the receiver is simplified

17

5.7 Delta Modulation

Delta-Sigma Modulation

18

5.8 Differential Pulse-Code Modulation

Prediction

• Samples at a rate higher than Nyquist rate con-tain redundant information.

• By removing this redundancy before encoding, we can obtain more efficient encoded signal.

• If we know the past behavior, it is possible to make some inference about its future values.

• Predictor

– : prediction of – : prediction error– Implemented by tapped-delay-line filter (discrete-time

filter)– : prediction order

19

)34.5()()()( sss nTmnTmnTe

5.8 Differential Pulse-Code Modulation

Prediction

20

5.8 Differential Pulse-Code Modulation

Differential Pulse-Code Modulation

21

5.8 Differential Pulse-Code Modulation

Differential Pulse-Code Modulation

• Differential pulse-code modulation (DPCM)– Oversampling + differential quantization + encoding– The input of differential quantization is the prediction er-

ror.

• where is quantization error.

– (5.38) is regardless of the properties of the prediction fil-ter.

– If the prediction is good, the average power of will be smaller than Smaller quantization error

22

)35.5()()()( sssq nTqnTenTe

)36.5()()()( sqssq nTenTmnTm

)37.5()()()()( ssssq nTqnTenTmnTm

)38.5()()()( sssq nTqnTmnTm

5.9 Line Codes

Line Codes

• A line code is needed for electrical representation of a binary sequence.

• Several line codes– On-off signaling– Nonreturn-to-zero (NRZ)– Return-to-zero– Bipolar return-to-zero (BRZ)– Split-phase (Manchester code)– Differential encoding

23

5.9 Line Codes

Line Codes

24

On-off signaling

Non return-to-zero(NRZ)

Return-to-zero

Bipolar return to zero(BRZ)

Split-phase (Manchester code)

Differential encoding

5.9 Line Codes

Differential Encoding

25

Differential encoding

0: Transition1: No transition

Reference bit: 1