Finite Wordlength Design of IIR Filters using Particle Swarm Optimization

Abstract

Optimal design problems of IIR (Infinite Impulse Response) filters with finite word length are formulated as nonlinear discrete optimization problems, and as the filter order and the word length of coefficients increase, the calculation cost for solving this problem rises exponentially. Moreover, since the guarantee of stability is necessary in the IIR filter design, the additional calculation cost of this must also be considered. For solving these problems, we express the transfer functions of filters as the product (cascade connection) of second order rational functions to make the guarantee of stability easily, and propose an efficient solution method based on PSO for optimal design problems of such filters which can obtain an (approximate) optimal solution in practical time for high-order problems.