On Fast Randomly Generation of Population of Minimal Phase and Stable Biquad Sections for Evolutionary Digital Filters Design Methods

Abstract

Evolutionary algorithms possesses many practical applications. One of the practical application of the evolutionary methods is digital filters design. Evolutionary techniques are very often used to design FIR (Finite Impulse Response) digital filters or IIR (Infinite Impulse Response) digital filters. IIR digital filters are very often practically realized as a cascade of biquad sections. The guarantee of stability of biquad sections is one of the most important element during IIR digital filter design process. If we want to obtain a stable IIR digital filter, the all poles of the transfer function for all biquad sections must be located into the unitary circle in the z-plane. Of course, if we want to have a minimal phase digital filter then all zeros of the transfer function for all biquad sections must be also located into the unitary circle in the z-plane. In many evolutionary algorithms which are dedicated to the IIR digital filter design the initial population (or re-initialized populations) of the filter coefficients are chosen randomly. Therefore, some of digital filters which are generated in population can be unstable (or/and the filters are not minimal phase). In this paper, we show how to randomly generate a population of stable and minimal phase biquad sections with very high efficiency. Due to our approach, we can also reduce a computational time which is required for evaluation of stability (or/and minimal phase property) of digital filter. The proposed approach has been compared with standard techniques which are used in evolutionary digital filter design methods.