Almost uniformity of quantization errors

A short alternative derivation of the Fourier series representation of the density of the quantization error is given. The quantization error for the general Gaussian signal, N( mu , sigma /sup 2/), is considered and is analytically shown to be almost uniform for sigma / Delta >1 where Delta is the quantization step. The problem of estimating mu by quantized observations is considered. A class of distributions with almost uniform quantization error densities is introduced. Particular distributions in this class are the general Gaussian distribution, the gamma distribution, and the Cauchy distribution. A general class of signals and a second class of densities are shown to have almost uniform error densities. The general bivariate Gaussian distribution and certain kinds of multivariate signals have almost uniform quantization errors.<
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