Quantization Errors of Modulo Sigma-Delta Modulated ARMA Processes
Abstract
In this paper, we study the quantization errors of modulo sigma-delta modulated finite, asymptotically-infinite, infinite causal stable ARMA processes. We prove that the normalized quantization error can be taken as a uniformly distributed white noise for all the cases. Moreover, we find that this nice property is guaranteed by two different mechanisms: the high-enough quantization resolution \cite{Bennett1948}-\cite{WidrowKollar2008} and the asymptotic convergence of quantization errors for some quasi-stationary processes \cite{ChouGray1991}-\cite{LiChenLiZhang2009}, for different cases. But the assumption of the smooth density of the sampled random processes is needed in all the cases.
Cite
@article{arxiv.0908.0794,
title = {Quantization Errors of Modulo Sigma-Delta Modulated ARMA Processes},
author = {Li Li and Yudong Chen},
journal= {arXiv preprint arXiv:0908.0794},
year = {2016}
}
Comments
An abbreviated version of this paper had been published as Li Li, Yudong Chen, "Quantization errors of modulo sigma-delta modulated ARMA processes," Proceedings of IEEE China Summit & International Conference on Signal and Information Processing, pp. 86-90, 2013