Abstract :
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.
