Digital IIR filters with minimal group delay for real-time applications

Abstract

In this paper we examine the potential for designing digital (IIR) filters with minimal group delay, which are relevant for real-time applications. By formulating filter design as a multi-objective optimization problem and approaching it with an unbiased metaheuristic search algorithm, we have established relationships between filter delay and other filter objectives. These relationships are presented as non-inferior surfaces for different filter orders and design approaches. We present possible designs that are realizable with (1) classical IIR design constructions, and (2) unconstrained global search for filter orders between 2 and 5. Elliptical (Cauer) filters are found as to have the highest potential for low group delay among the classical constructions. However, as one might expect, unconstrained IIR search discovers more optimal filters, but is limited to filter orders of ~5. Currently, there exists no established method that can construct similar IIR filters with a group delay below n/2, where n is the given filter order. Finally, we present some unconstrained filter examples that we claim are nearly optimal.