Asymptotic analysis of optimum uniform scalar quantizers for generalized Gaussian distributions

摘要

This paper studies the asymptotic characteristics of optimum uniform scalar quantizers as N, the number of levels, becomes large. It is shown that the length of the support region increases as (ln N)/sup 1//spl alpha//, when applied to a random variable with a generalized Gaussian density of the form p(x)=ae(-b|x|/sup /spl alpha//). Moreover, the mean-squared error is asymptotically well approximated by /spl Delta//sup 2//12, where /spl Delta/ is the step size, and decreases as (ln N)/sup 2//spl alpha///N/sup 2/.