A New Mutated Quantum-Behaved Particle Swarm Optimizer for Digital IIR Filter Design

Wei Fang,Jun Sun,Wenbo Xu

doi:10.1155/2009/367465

Abstract

Adaptive infinite impulse response (IIR) filters have shown their worth in a wide range of practical applications. Because the error surface of IIR filters is multimodal in most cases, global optimization techniques are required for avoiding local minima. In this paper, we employ a global optimization algorithm, Quantum-behaved particle swarm optimization (QPSO) that was proposed by us previously, and its mutated version in the design of digital IIR filter. The mechanism in QPSO is based on the quantum behaviour of particles in a potential well and particle swarm optimization (PSO) algorithm. QPSO is characterized by fast convergence, good search ability, and easy implementation. The mutated QPSO (MuQPSO) is proposed in this paper by using a random vector in QPSO to increase the randomness and to enhance the global search ability. Experimental results on three examples show that QPSO and MuQPSO are superior to genetic algorithm (GA), differential evolution (DE) algorithm, and PSO algorithm in quality, convergence speed, and robustness.

Highlights

Adaptive infinite impulse response (IIR) filters have been proven to be useful in many fields such as channel equation, noise reduction, echo cancelling, and system identification [1, 2]
genetic algorithm (GA), differential evolutionary (DE), and particle swarm optimization (PSO) algorithm are used for the digital IIR filter design in order to make a performance comparison with Quantum-behaved Particle Swarm Optimization (QPSO) and mutated version of QPSO (MuQPSO)
We have introduced the new global optimization technique, QPSO, and proposed its variation, MuQPSO

Summary

Introduction

Adaptive IIR filters have been proven to be useful in many fields such as channel equation, noise reduction, echo cancelling, and system identification [1, 2]. As a variant of PSO, Quantum-behaved Particle Swarm Optimization (QPSO) was proposed [14, 15] in 2004. It is inspired by quantum mechanics and fundamental theory of particle swarm It is convenient for PSO and QPSO to apply in the digital IIR filter design as the design can be reduced to a minimization problem and solved by these algorithms. A mutated version of QPSO (MuQPSO) is proposed by introducing a random vector in QPSO in order to enhance the randomness and global search ability. Both QPSO and MuQPSO are applied to digital IIR filter design.

QPSO and Its Mutated Version

Application of QPSO and MuQPSO to the Design Problem

Conclusions