Application of the Fokker-Planck-Kolmogorov equation to the analysis of differential pulse code modulation systems

Abstract

A representation of a Differential Pulse Code Modulation (DPCM) system with a uniform quantizer is given such that the “slope overload” and “granular” effects are separated. This representation includes a continuous feedback loop describing the “overload” effect followed by a parallel connection of appropriate samplers and quantizers, describing the “granular” effect. The granular noise is known to have approximately a flat spectrum over the signal band and a uniform probability density function. The spectrum of the slope overload noise as well as its probability density function is not known. Using the above representation a study of the probability density function of the slope overload noise is presented for an input which is a vector Gauss-Markov process. This study uses methods known in control theory. Explicit results are presented for certain input processes with simple spectra. Some applications of continuous Markov processes to this problem are discussed.