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610 Chapter 12 APPLICATIONS IN COMMUNICATIONS
In the reconstruction of the signal from the quantized values, the
decoder employs an inverse logarithmic relation to expand the signal
amplitude. For example, in µ-law the inverse relation is given by
|s| = (1 + µ)|y| − 1
; |y| ≤1, |s| ≤1 (12.7)
µ
The combined compressor-expander pair is termed a compander.
12.1.1 PROJECT 12.1: PCM
The purpose of this project is to gain an understanding of PCM compression
(linear-to-logarithmic) and PCM expansion (logarithmic-to-linear).
Write the following three MATLAB functions for this project:
1. a µ-law compressor function to implement (12.5) that accepts a zeromean
normalized (|s| ≤1) signal and produces a compressed zero-mean
signal with µ as a free parameter that can be specified,
2. a quantizer function that accepts a zero-mean input and produces an
integer output after b-bit quantization that can be specified, and
3. a µ-law expander to implement (12.7) that accepts an integer input
and produces a zero-mean output for a specified µ parameter.
For simulation purposes generate a large number of samples (10,000
or more) of the following sequences: (a) a sawtooth sequence, (b) an exponential
pulse train sequence, (c) a sinusoidal sequence, and (d) a random
sequence with small variance. Care must be taken to generate nonperiodic
sequences by choosing their normalized frequencies as irrational numbers
(i.e., sample values should not repeat). For example, a sinusoidal sequence
can be generated using
s(n) =0.5 sin(n/33), 0 ≤ n ≤ 10,000
From our discussions in Chapter 2, this sequence is nonperiodic, yet it
has a periodic envelope. Other sequences can also be generated in a similar
fashion. Process these signals through the above µ-law compressor,
quantizer, and expander functions as shown in Figure 12.2, and compute
FIGURE 12.2
PCM project
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