PCM Reference – Stremler, Communication Systems, Chapter 7.4-7.6

K.1

Pulse-code modulation (PCM) Pulse modulations use discrete time samples of analog signals. In these cases, 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. In PCM, the analog signal is quantized into a number discrete levels.

K.2

1

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

8 7 6 5 4 3 2 1 0

t

Digits

K.3

This process of quantization introduces some fluctuations about the true value; these fluctuation can be regarded as nosise and called quantiztion noise.

K.4

2

– 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. Binary Digits code 000 0 1

001

2

010

3

011

4

100

5

101

6

110

7

111 K.5

Quantization noise Consider an input f (t ) of continuous amplitude in the range (− f max , f max ). Assuming using a uniform quantizer, the step-size of the quantizer is ∆ = 2 f max / L where L is the total number of representation levels. ∆

2 f max

K.6

3

For a uniform quantizer, the quantization error q is bounded by . − ∆/2 ≤ q ≤ ∆/2 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:  1 p(q) =  ∆  0

∆ ∆