Analysis of Adaptive Differential PCM (Pulse-Code Modulation) of a Stationary Gauss-Markov Input

摘要

An adaptive matched differential pulse-code modulator (AMDPCM) is analyzed. The adaptation of the symmetric uniform quantizer parameter Delta sub n is performed by fixed multipliers assigned to the quantizer output levels. The input is stationary first-order Gauss-Markov. The correlation of the samples is used as the leakage parameter in the matched integrator, with the predictive reconstruction similarly matched For a 4-level quantizer and multipliers 1/gamma; gamma the limiting joint distribution of the prediction error and Delta sub n is derived and the asymptotic sample-point and time-averaged mean-square error (mse) and mean and variance of Delta sub n as functions of gamma is an element of (1,2) are computed and plotted. It is found that asymptotic performance of AMDPCM does not depend on the choice of Delta sub 0 that the increase in mse incurred by using A(M)DPCM instead of (M)DPCM with Delta sub opt is small. with mse (A(M)DPCM approaching min sub Delta mse (M)DPCM) as gamma approaches 1 and that the signal-to-noise ratio of AMDPCM does not depend on the input power.