The zero-input response of digital filters using saturation arithmetic

In this paper we observe that a recent extension to certain higher order cases of saturized arithmetic (quantization is ignored in the idealized model) is a direct corollary of a theorem in the theory of feedback systems, and that the extension (and related more general propositions) can be proved without the earlier theorem by using simple operator-theoretic methods. The main result given in the paper is an extension of the result for nonidealized second-order sections to a class of filters of arbitrary order.