Design of low complexity FIR filters using genetic algorithms and directed graphs

This paper examines the use of Genetic Algorithms (GAs) to design low complexity, primitive operator, digital FIR filters. Most previous design methods have involved a two stage approach of either optimizing the performance for a given filter structure, or optimizing the architecture for a given filter. In this paper we present a joint optimization of both structure and performance which can yield improvements over both of these techniques. The proposed method uses a primitive operator directed graph implementation which allows a reduction in complexity compared to alternative techniques, using canonic signed digit (CSD), or signed power-of-two (SPT) representation. In order to simplify the problem, a heuristic graph design algorithm is used to calculate implementational complexity of candidate filters. The GA is then used to optimize sets of integer filter coefficients, in order to find a non dominated set of solutions which provide various trade-offs between complexity, filter order, and performance. Example one-dimensional linear phase filters are designed and compared to previous designs using alternative techniques.