Title :
Asymptotic analysis of optimum uniform scalar quantizers for generalized Gaussian distributions
Author :
Hui, Dennis ; Neuhoff, David L.
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA
fDate :
27 Jun-1 Jul 1994
Abstract :
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)1 α/, when applied to a random variable with a generalized Gaussian density of the form p(x)=ae(-b|x|α). Moreover, the mean-squared error is asymptotically well approximated by Δ 2/12, where Δ is the step size, and decreases as (ln N) 2α//N2
Keywords :
Gaussian distribution; quantisation (signal); statistical analysis; asymptotic analysis; asymptotic characteristics; generalized Gaussian density; generalized Gaussian distributions; mean-squared error; optimum uniform scalar quantizers; random variable; step size; support region length; Analysis of variance; Computer science; Gaussian distribution; H infinity control; Integral equations; Laplace equations; Lattices; Probability density function; Random variables; Vector quantization;
Conference_Titel :
Information Theory, 1994. Proceedings., 1994 IEEE International Symposium on
Conference_Location :
Trondheim
Print_ISBN :
0-7803-2015-8
DOI :
10.1109/ISIT.1994.395076
