Synthesis Tool Based on Genetic Algorithm for FIR Filters with User-Defined Magnitude Characteristics

Abstract

This paper presents a method for synthesizing linear-phase FIR filters capable of implementing magnitude characteristics defined arbitrarily by the user through a set of frequency---magnitude points, filters that are optimized with respect to several criteria. The main idea is to approach the filter synthesis as a multi-objective optimization problem, targeting the minimization of both the peak magnitude and the total squared errors of the resulting magnitude characteristics, as well as implementation-related requirements such as the reduction of the filter length. The optimization procedure uses a genetic algorithm tailored to this application; it employs a novel encoding scheme for the filter chromosome and an efficient fitness function, based on only two well-chosen constraints. Several design examples are presented: first, optimized synthesis of FIR filters with magnitude characteristics that match given (arbitrary) human audiograms, and second, synthesis of filters defined by parameters related to their pass- and stop-bands. The results yielded by the proposed method compare well with filters synthesized by means of previously reported methods and an industry-standard MATLAB tool.