1. Chapter 5. Pulse Modulation
From Analog to Digital

2. 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

3. 5.6 Pulse-Code Modulation Pulse-Code Modulation

4. 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 amplitude appear frequently whereas large amplitude is rare.
Nonuniform quantizer is equivalent to compressor followed by uniform quantizer.

5. 5.6 Pulse-Code Modulation Operations in the Transmitter
𝜇–law compressor
𝐴-law compressor

6. 5.6 Pulse-Code Modulation Operations in the Transmitter

7. 𝝁–law compressor Quantization |m| μ=0.01 μ=5 μ=20 μ=100 0.00 0.05 0.13
|v|
μ=0.01
μ=5
μ=20
μ=100
0.00
0.05
0.13
0.23
0.56
0.10
0.36
0.69
0.15
0.31
0.46
0.75
0.20
0.39
0.53
0.80
0.25
0.45
0.59
0.83
0.30
0.51
0.64
0.86
0.35
0.57
0.68
0.88
0.40
0.61
0.72
0.90
0.66
0.76
0.91
0.50
0.70
0.79
0.92
0.55
0.74
0.82
0.94
0.60
0.77
0.84
0.95
0.65
0.81
0.87
0.89
0.96
0.97
0.93
0.98
0.85
0.99
1.00
Output level
Quantization
Input level

8. 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

9. 5.6 Pulse-Code Modulation Operations in the Transmitter

10. 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

11. 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 complementary to the compressor
The combination of a compressor and an expander is called a compander.
Reconstruction
Recover the message signal by passing the expander output through a low-pass reconstruction filter

12. 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 (±Δ)
where 𝑒 𝑛 𝑇 𝑠 is an error signal

13. 5.7 Delta Modulation Basic Considerations

14. 5.7 Delta Modulation System Details
Comparator
Computes the difference between its two inputs
Quantizer
Consists of a hard limiter with an input-output characteristic 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

15. 5.7 Delta Modulation System Details

16. 5.7 Delta Modulation Quantization Errors
Slope-overload distortion
Occurs when the step size is too small
The approximation signal falls behind the message signal
Granular noise
Occurs when the step size is too large
The staircase approximation hunts around a flat segment.

17. 5.7 Delta Modulation Delta-Sigma Modulation
Drawback of DM
An accumulative error in the demodulated signal
Delta-sigma modulation (D-ΣM)
Integrates the message signal prior to delta modulation
Benefit of the integration
The low-frequency content of the input signal is pre-emphasized
Correlation between adjacent samples of the delta modulator input is increased
Design of the receiver is simplified

18. 5.7 Delta Modulation Delta-Sigma Modulation

19. 5.8 Differential Pulse-Code Modulation Prediction
Samples at a rate higher than Nyquist rate contain 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
𝑚 (𝑛 𝑇 𝑠 ): prediction of 𝑚 𝑛 𝑇 𝑠
𝑒 𝑛 𝑇 𝑠 : prediction error
Implemented by tapped-delay-line filter (discrete-time filter)
𝑝: prediction order

20. 5.8 Differential Pulse-Code Modulation Prediction

21. 5.8 Differential Pulse-Code Modulation Differential Pulse-Code Modulation

22. Differential pulse-code modulation (DPCM)
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 error.
where 𝑞 𝑛 𝑇 𝑠 is quantization error.
(5.38) is regardless of the properties of the prediction filter.
If the prediction is good, the average power of 𝑒 𝑛 𝑇 𝑠 will be smaller than 𝑚(𝑛 𝑇 𝑠 )  Smaller quantization error

23. 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

24. Bipolar return to zero(BRZ) On-off signaling
5.9 Line Codes Line Codes
Bipolar return to zero(BRZ)
On-off signaling
Split-phase (Manchester code)
Non return-to-zero(NRZ)
Return-to-zero
Differential encoding

25. 5.9 Line Codes Differential Encoding
0: Transition
1: No transition
Reference bit: 1
Differential encoding