Quantization errors of modulo sigma-delta modulated ARMA processes

In this paper, we study the quantization errors of modulo sigma-delta modulated finite, asymptotically-infinite, infinite causal stable ARMA processes. We show 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 and the asymptotic convergence of quantization errors for some quasi-stationary processes, for different cases. But the assumption of the smooth density of the sampled random processes is needed in all the cases.