PCM Reference Chapter 1.1, Communication Systems, Carlson. PCM.1
Pulse-code modulation (PCM) Pulse modulations use discrete time samples of analog signals the transmission is composed of analog information sent at discrete times. The variation of pulse amplitude or pulse timing is allowed to vary continuously over all values. PCM the analog signal is quantized into a number discrete levels. PCM.
Example: Suppose that we wish to quantize a signal using eight discrete levels. At each sample time we must decide which of these eight levels is best approximation to the signal. We choose the closest value and use this value until the next sample time. Quantization noise t 8 7 6 4 5 3 1 0 Digits PCM.3
This process of quantization introduces some fluctuations about the true value; these fluctuation can be regarded as noise and called quantization noise. PCM.4
The next step is to assign a digit to each level. This is called digitization of the waveform. The digits are expressed in a coded form. The most common code used is a binary code. Digits 0 1 3 4 5 6 7 Binary code 000 001 010 011 100 101 110 111 PCM.5
Quantization noise Consider an input f (t) of continuous amplitude in the range ( f max, fmax ). Assuming using a uniform quantizer, the step-size of the quantizer is = f max / L where L is the total number of representation levels. f max PCM.6
For a uniform quantizer, the quantization error q is bounded by. / q / If the step-size is sufficient small, it is reasonable to assume that the quantization error is a uniformly distributed random variable, and the interfering effect of the quantization noise on the quantizer input is similar to that of thermal noise. We may express the probability density function of the quantization error as: p( q) = 1 0 < q < otherwise PCM.7
Therefore, the average power of the quantization noise is n q = = = / / 1 1 q / / p( q) dq q dq PCM.8
Example: Consider a full-load sinusoidal modulating signal of amplitude A, which utilizes all the representation levels provided. The average signal power is P = A The total range of the quantizer is A because the modulating signal swings between -A and A. Therefore, if it is a 4-bit quantizer, A = 4 = A 8 PCM.9
and the quantization noise is n = = 1 A 768 The S/N ratio is ( A / ) ( A / 768) = 384 = 5.8dB PCM.10
Nonuniform quantizing Uniform quantizaiton The S/N ratio is low for low level signal In telephone system, nonuniform quantizers are used Increase the S/N ratio for low level signal Example: Smaller range f max PCM.11
Nonuniform quantizing Nonuniform quantizer Equivalent to passing the baseband signal through a compressor and then applying the compressed signal to a uniform quantizer. output Compressor for the uniform quantizer input For uniform quantizer PCM.1
Nonuniform quantizing Compressor law µ-law log(1 + µ m v = log(1 + µ ) ) v 1 µ = 5 µ = 0 0 1 m PCM.13
Nonuniform quantizing Compressor law A-law v = A m 1+ log A 1+ log( A m ) 1+ log A 1 0 m A 1 m 1 A At the receiver An expander is used to restore the signal. The combination of a compressor and an expander is called a compander PCM.14
Advantages of PCM (digital communications) In long-distance communications, PCM signals can be completely regenerated at intermediate repeater stations because all the information is contained in the code. Essentially a noise-free signal is retransmitted at each repeater. The effects of noise do not accumulate and one need to concerned only about the effects of transmission noise between adjacent repeaters. Modulating and demodulating circuitry is all digital, thus affording high reliability and stability, and is readily adapted to integrated-circuit logic design. PCM.15
Signals may be stored and time scaled efficiently. 100Mbps link music 100 kbps source for 100 seconds = 10 Mbps Transmit time=0.1s Playback time = 10s Efficient codes can be utilized to reduce unnecessary repetition (redundancy) in messages. (source coding) 1 01 001 0001 00001 000001 0000001 0000000 Source Encoder 000 001 010 011 100 101 110 111 PCM.16
Appropriate coding can reduce the effects of noise and interference. (channel coding) Example: 1 encoded as 111 and 0 encoded as 000 101 Channel 111000111 Encoder Noisy Channel 101 The errors are removed Receiver 110010111 Errors PCM.17