Optimizing Continued Fraction Expansion Based IIR Realization of Fractional Order Differ-Integrators with Genetic Algorithm

TL;DR

This paper presents an optimization approach using Genetic Algorithms to improve the rational approximation of fractional order differ-integrators via Continued Fraction Expansion, resulting in more accurate IIR filter realizations.

Contribution

It introduces a novel optimization method that enhances the approximation accuracy of FO differ-integrators in IIR filters compared to existing techniques.

Findings

Optimized filters exhibit lower magnitude and phase deviation.

Frequency response analysis confirms improved approximation.

Genetic Algorithm effectively fine-tunes generating functions.

Abstract

Rational approximation of fractional order (FO) differ-integrators via Continued Fraction Expansion (CFE) is a well known technique. In this paper, the nominal structures of various generating functions are optimized using Genetic Algorithm (GA) to minimize the deviation in magnitude and phase response between the original FO element and the rationalized discrete time filter in Infinite Impulse Response (IIR) structure. The optimized filter based realizations show better approximation of the FO elements in comparison with the existing methods and is demonstrated by the frequency response of the IIR filters.