A Genetic Algorithm for the Design and Optimization of FRM Digital Filters Over a Canonical Double-Base Multiplier Coefficient Space

Abstract

Double-base number systems (DBNSs) have recently gained recognition for the hardware implementation of low-power digital signal processing systems. This paper presents a genetic algorithm for the design of frequency response masking (FRM) digital filters over a single-digit DBNS system. This is based on designing a corresponding seed infinite precision coefficient digital filter (through continuous optimization), and on quantizing the resulting multiplier coefficients into single-digit DBNS coefficients via a look-up table. The resulting digital filter is 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 DBNS 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 FRM digital filter produces a DBNS-coefficients digital filter with superior performance to that obtained by continuous optimization.