Automated design of low complexity FIR filters

This paper considers the design of low complexity FIR filters. Complexity is reduced by constraining the filters to have integer coefficients, which can be efficiently implemented using primitive operator directed graphs (PODG). Genetic algorithms (GAs) are used in conjunction with a heuristic graph design algorithm, to provide a solution set which represents different compromises between performance, complexity and filter order. Example results are presented for both one and two dimensional filters, and are shown to provide both superior performance and complexity, compared to previous methods. The main benefits result from the use of a joint optimization, rather than a separable 2-stage approach. The use of a PODG representation is shown to provide significant improvements over a canonic signed digit (CSD) or signed power-of-two (SPT) representation