An Algorithm for the Design of Multiplierless IIR Filters as a Parallel Connection of Two All-Pass Filters

This paper describes an algorithm for designing multiplierless recursive digital filters as a parallel connection of two all-pass filters. The coefficient optimization is performed in two steps. First, simple closed-form algebraic expressions are used for determining a parameter space of the infinite-precision coefficients including the feasible space where the filter meets the given criteria. The second step uses genetic algorithm for finding the filter parameters in this space so that the resulting filter meets the given criteria with the simplest coefficient representation forms. Two implementation structures are under consideration, namely, the all-pass transfer functions are implemented either using Stoyanov-Kawamata or Gray-Markel all-pass sections. Comparisons with some other existing quantization schemes show that the proposed algorithm gives better finite-precision solutions in all examples taken from the literature