Quantization Errors of Modulo Sigma-Delta Modulated ARMA Processes

TL;DR

This paper analyzes the quantization errors in modulo sigma-delta modulated ARMA processes, demonstrating that these errors behave like white noise under certain conditions, with implications for signal processing accuracy.

Contribution

It proves that quantization errors in these processes are uniformly distributed white noise, highlighting mechanisms like high-resolution quantization and asymptotic convergence.

Findings

Quantization errors can be modeled as white noise.

High-resolution quantization ensures error uniformity.

Asymptotic convergence applies to quasi-stationary 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.