Quantization Errors of Modulo Sigma-Delta Modulated ARMA Processes

Li Li; Yudong Chen

doi:10.1109/chinasip.2013.6625303

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arXiv · 0908.0794

Quantization Errors of Modulo Sigma-Delta Modulated ARMA Processes

Li Li·Yudong Chen

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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.

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Li Li, Yudong Chen. 2014-06-07. Quantization Errors of Modulo Sigma-Delta Modulated ARMA Processes. https://doi.org/10.1109/chinasip.2013.6625303

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