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

5.6 Pulse-Code Modulation Pulse-Code Modulation

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.

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

5.6 Pulse-Code Modulation Operations in the Transmitter

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

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

5.6 Pulse-Code Modulation Operations in the Transmitter

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

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

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

5.7 Delta Modulation Basic Considerations

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

5.7 Delta Modulation System Details

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.

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

5.7 Delta Modulation Delta-Sigma Modulation

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

5.8 Differential Pulse-Code Modulation Prediction

5.8 Differential Pulse-Code Modulation Differential Pulse-Code Modulation

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

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

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

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