A Novel Diversity-Controlled Genetic Algorithm for Rapid Optimization of Bandpass FRM FIR Digital Filters Over CSD Multiplier Coefficient Space

Abstract

The conventional frequency response masking (FRM) approach is one of the most well-known techniques for the design of sharp transition band finite impulse response (FIR) digital filters. The resulting FRM digital filters permit efficient hardware implementations due to an inherently large number of zero-valued multiplier coefficients. The hardware complexity of these digital filters can further be reduced by representing the remaining (non-zero) multiplier coefficient values by using their canonical signed-digit (CSD) representations. This paper presents a novel diversitycontrolled (DC) genetic algorithm (GA) for the discrete optimization of bandpass FRM FIR digital filters over the CSD multiplier coefficient space. The resulting bandpass FIR digital filters are permitted to have equal or unequal lower and upper transition bandwidths. The proposed DCGA is based on an indexed look-up table of permissible CSD multiplier coefficients such that their indices form a closed set under the genetic operations of crossover and mutation. The salient advantage of DCGA over the conventional GA lies in the external control over population diversity and parent selection, giving rise to a rapid convergence to an optimal solution. The external control is achieved through the judicious choice of a pair of DCGA optimization parameters. An empirical investigation is undertaken for choosing appropriate values for these control parameters. The convergence speed advantages of the DCGA are demonstrated through its application to the design and optimization of a pair of bandpass FRM FIR digital filters with equal or arbitrary lower and upper transition 600 Circuits Syst Signal Process (2008) 27: 599-625 bandwidths. In both cases, an increase of about an order of magnitude in the speed of convergence is achieved as compared to the conventional GAs.

A Novel Diversity-Controlled Genetic Algorithm for Optimization of BIBO Stable Digital IF Filters Over CSD Multiplier Coefficient Space

“…In the absence of analytical solutions, the values of the shape coefficient c and the exponent parameter α are usually selected through an empirical investigation. This investigation is conducted over suitable range of values for c and α [10].…”

“…The selection of such chromosomes increases the diversity of the population pool, giving rise to a substantial increase in the convergence speeds [16]. In particular, if the fitness function has a few local optima only, then by using a high value of c and/or small value of α, one can achieve a rapid convergence to an optimal solution [10]. On the other hand, when the fitness function is multimodal, lower values of c and/or higher values of α can be chosen to increase the probability of selecting chromosomes that are different from the chromosome with the highest fitness value [10].…”

“…It is well known that GAs provide a promising approach to solve discrete and multimodal optimization problems due to the fact that they are capable of automatically finding near-optimal solutions while keeping the computational complexity of the optimization at moderate levels [9]. Consequently, they have emerged as an efficient alternative for the optimization of finite impulse-response (FIR) and IIR digital filters [10]. These algorithms encode the digital filter realization into a chromosome, and proceed toward an optimal solution through the evolution of a population of potential candidate chromosomes iteratively from one generation to the next.…”