  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.
