Sampling and Quantization - Digital Speech: Coding for Low Bit Rate Communication Systems - page 29

111

y8

Output

110

y7

101

y6

100

y5

x1 x2 x4 x5 x6 x7

x3

011

y4

Input

010

y3

001

y2

000

y1

Figure 3.3 The input-output characteristics of a nonuniform quantizer

compressor, C(x) , compresses the input samples depending on their statistical
properties. In otherwords, the less likely higher sample values are compressed
more than the more likely low amplitude samples. The compressed samples
are then quantized using a uniform quantizer. The effect of compression
is reversed at the receiver by applying the inverse C − 1 (x) expansion to the
de-quantized samples. The compression and expansion processes do not
introduce any signal distortions.
It is quite important to select the best compression-expansion combination
for a given input signal probability density function. Panter and Dite [3]
used analysis based on the assumption that the quantization is sufficiently
fine and that the amplitude probability density function of the input samples
is constant within the quantization intervals. Their results show significant
improvement in the signal to noise ratio over uniform quantization if the
input samples have a peak to root mean squared ( rms ) ratio greater than 4.
In designing an optimum quantizer, Max [4] discovered how to optimally
choose the output levels for nonuniform input quantizer levels. His analysis
requiredprior knowledge of the probability density function togetherwith the