Optimization of IIR Digital Filters Using Differential Evolution: A Comparative Analysis of FDDE and AMECoDEs Algorithms

Abstract

Infinite impulse response (IIR) digital filters are fundamental components in various digital signal processing applications, particularly those requiring optimized use of computational resources, such as memory and processing power. This study presents the design of classical IIR filters, including low-pass, high-pass, band-pass, and band-stop configurations, as well as multiple-passband filters featuring dual and triple passbands. Two differential evolution algorithms are utilized: FDDE (Differential Evolution Algorithm with Fitness and Diversity Ranking-Based Mutation Operator) and AMECoDEs (Adaptive Multiple-Elites-Guided Composite Differential Evolution Algorithm with a Shift Mechanism). To date, no study has investigated the application of the FDDE algorithm to IIR digital filter design, whereas the AMECoDEs algorithm has seen limited application in this context. Consequently, this work investigates the design of IIR filters using these algorithms and assesses their performance based on the mean squared error (MSE). Comparative analysis reveals that, for classical filters, the FDDE algorithm yields a slightly lower MSE in the magnitude response compared to the AMECoDEs algorithm. Conversely, for multiple-passband filters, the AMECoDEs algorithm outperforms FDDE by achieving a lower MSE. In the proposed model, IIR filters are implemented using a cascade structure of second-order sections (SOS), with their fitness function evaluated based on the MSE, computed using a constant weight function within each frequency band. Additionally, the magnitude response characteristics of the designed filters are compared with those of classical and dual-passband filters designed with the AMECoDEs algorithm in recent studies. The results indicate that the filters designed in this study show significant improvements across most evaluated metrics, particularly in terms of improved stopband attenuation. One of the key contributions of this work is the novel application of differential evolution algorithms to the design of triple-passband IIR filters, demonstrating their effectiveness through successful validation on a development board.