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(μ,σ² ), is considered and is analytically shown to be almost uniform for σ/Δ>1 where Δ is the quantization step. The problem of estimating μ 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