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

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 this 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 maximizing the derived stability-related measure