On the structure of digital filters with stability and roundoff noise consideration

In this paper, the stability behavior and error propagation of a digital filter implemented with Finite WordLength are investigated. Based on a first order approximation, a stability robustness related measure is derived. This measure is shown to be filter structure dependent. The optimal structures are defined as those that, maximize measure. A class of solutions is given. The roundoff noise gain is a measure of error propagation. The, minimum roundoff noise structures are obtained subject to maxmizing the derived stability related measure.