Variants of Genetic Algorithm for Efficient Design of Multiplier-Less Finite Impulse Response Digital Filter

Background

Design of discrete coefficient digital FIR filters has drawn considerable attention of the researchers since last three decades. The very first article addressing this issue was published in the year 1982 by Lim and his co-researchers who had proposed an idea of Mixed Integer Linear Programming (MILP) for designing finite word-length FIR filters (Lim, 1982). Similar work has shortly been facilitated by Weighted Least Square (WLS) method and local search technique in few years (Lim, 1983). These methods suffers from serious drawbacks in terms of computational complexity as the number of computation increases exponentially with the filter order and hence limits its application in synthesizing filters of higher length. Later on, scientists have thought to start with a given optimal filter solution and subsequently identified finite word-length solution in the neighborhood of an optimal solution that will minimize the computational cost. This simplest scheme of truncating the coefficients to a fixed-bit representation has not come up with a reliable solution since the frequency response of these filters seems to be significantly affected by the process of coefficient quantization.