Design of FRM digital filters over the CSD multiplier coefficient space employing genetic algorithms

It is well known that the use of canonical signed-digit (CSD) multiplier coefficients in combination with sub-expression sharing and elimination leads to a substantial reduction in the hardware complexity of FIR digital filters. This paper presents a genetic algorithm for the design and optimization of frequency-response masking (FRM) FIR digital filters over the CSD multiplier coefficient space. This is based on designing a corresponding infinite-precision-coefficient digital filter seed (through a conventional continuous optimization), and on quantizing the resulting multiplier coefficients into CSD coefficients via a look-up table. The resulting digital filter is subsequently encoded into a chromosome which is perturbed to form an initial population for the genetic algorithm. The salient feature of the resulting genetic algorithm is that it automatically leads to legitimate CSD-coefficient offspring digital filters after the operations of crossover and mutation, i.e. without any recourse to gene repair. Application to the design of a bandpass FIR digital filter produces a CSD-coefficients digital filter with very close performance to that obtained by the corresponding continuous infinite-precision optimization