Optimization of FRM FIR Digital Filters Over CSD and CDBNS Multiplier Coefficient Spaces Employing a Novel Genetic Algorithm

Abstract

It is well known that frequency response masking (FRM) FIR digital filters can be designed to exhibit very sharp-transition bands at the cost of slightly larger filter lengths as compared to the conventional FIR digital filters. The FRM FIR digital filters permit efficient hardware implementations due to an inherently large number of zerovalued multiplier coefficients in their transfer functions. The hardware complexity of these FIR digital filters can be further reduced by employing computationally efficient number systems for the representation of the constituent non-zero-valued multiplier coefficients. This paper presents a novel genetic algorithm for the design and discrete optimization of FRM FIR digital filters over the conventional canonical signed-digit (CSD) as well as the emerging double base number system (DBNS) multiplier coefficient spaces. This genetic algorithm is based on a pair of indexed look-up tables (LUTs) of permissible CSD/DBNS numbers whose indices form a closed set under the genetic algorithm operations of crossover and mutation. The CSD/DBNS values themselves permit pre-specified word-lengths and pre-specified number of non-zero bits. The salient feature of the proposed genetic algorithm is that it automatically leads to legitimate CSD/DBNS multiplier coefficients without any recourse to gene repair during optimization. The main features of the proposed genetic algorithm are demonstrated through its application to the design of a pair of low-pass and band-pass FRM FIR digital filters.