A Novel DCGA Optimization Technique for Guaranteed BIBO-Stable Frequency-Response Masking Digital Filters Incorporating Bilinear Lossless Discrete-integrator IIR Interpolation Sub-Filters

Abstract

This work is concerned with the development of a novel diversity-controlled (DC) genetic algorithm (GA) for the design and rapid optimization of frequency-response masking (FRM) digital filters incorporating bilinear lossless discrete-integrator (LDI) IIR interpolation sub-filters. The selection of FRM approach is inspired by the fact it lends itself to the design of practical sharp-transition band digital filters in terms of gradual-transition band FIR interpolation sub-filters. The proposed DCGA optimization is carried out over the canonical-signed-digit (CSD) multiplier coefficient space, resulting in FRM digital filters which are capable of direct implementation in digital hardware. A novel CSD look-up table (LUT) scheme is developed so that in every stage of DCGA optimization, the IIR interpolation sub-filters constituent in the intermediate and final FRM digital filters are guaranteed to be automatically BIBO stable. The proposed DCGA optimization permits simultaneous optimization of the magnitude-frequency as well of the group-delay frequency response of the desired FRM digital filters. An example is given to illustrate the application of the resulting DCGA optimization to the design of a lowpass FRM digital filter incorporating a fifth-order bilinear-LDI interpolation subfilter.