In this problem, we use computer simulation to compare the performance of a companded PCM system using the -law against that of the corresponding system using a uniform quantizer. The simulation is to be performed for a sinusoidal input signal of varying amplitude.
With a companded PCM system in mind, Table describes the 15-segment pseudo-linear characteristic that consists of 15 linear segments configured to approximate the logarithmic -law of (6.48), with = 255. This approximation is constructed in such a way that the segment endpoints in Table 6.4 lie on the compression curve computed from (6.48).
a. Using the -law described in Table, plot the output signal-to-noise ratio as a function of the input signal-to-noise ratio, both ratios being expressed in decibels.
b. Compare the results of your computation in part (a) with a uniform quantizer having 256 representation levels.
