A Fuzzy Gravitational Search Algorithm to Design Optimal IIR Filters

Danilo Pelusi,Luca Tallini,Raffaele Mascella

doi:10.3390/en11040736

Danilo Pelusi, Luca Tallini + Show 1 more

Open Access

https://doi.org/10.3390/en11040736

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Journal: Energies	Publication Date: Mar 23, 2018
Citations: 21	License type: CC BY 4.0

Affiliation: University of Teramo

Abstract

The goodness of Infinite Impulse Response (IIR) digital filters design depends on pass band ripple, stop band ripple and transition band values. The main problem is defining a suitable error fitness function that depends on these parameters. This fitness function can be optimized by search algorithms such as evolutionary algorithms. This paper proposes an intelligent algorithm for the design of optimal 8th order IIR filters. The main contribution is the design of Fuzzy Inference Systems able to tune key parameters of a revisited version of the Gravitational Search Algorithm (GSA). In this way, a Fuzzy Gravitational Search Algorithm (FGSA) is designed. The optimization performances of FGSA are compared with those of Differential Evolution (DE) and GSA. The results show that FGSA is the algorithm that gives the best compromise between goodness, robustness and convergence rate for the design of 8th order IIR filters. Moreover, FGSA assures a good stability of the designed filters.

Highlights

The design of optimal Infinite Impulse Response (IIR) digital filters is a very interesting challenge
Because the quality of a IIR filter depends on pass band ripple, stop band ripple and transition band, we propose a new fitness function that takes into account these three parameters
An intelligent algorithm able to optimize the design of 8th order IIR filters has been described

Summary

Introduction

The design of optimal Infinite Impulse Response (IIR) digital filters is a very interesting challenge. The main techniques to design IIR filters are traditional design technique and optimization techniques. The second approach regards the applications of optimization techniques to design optimal filters. The steepest-descent and quasi-Newton (QN) algorithms are used for IIR filters design [1,2]. Because QN optimization approach is very flexible, it can be used to design filters with arbitrary amplitude and/or phase responses. QN algorithms have been used to design linear-phase IIR filters [3]. Chen et al [4] proposed a technique for IIR filters design based on the minimization the error between the order-reduced filter’s response and the desired one in the Hankel-norm sense

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