Phase Response Design of Recursive All-Pass Digital Filters Using a Modified PSO Algorithm.

Wei-Der Chang

doi:10.1155/2015/638068

Abstract

This paper develops a new design scheme for the phase response of an all-pass recursive digital filter. A variant of particle swarm optimization (PSO) algorithm will be utilized for solving this kind of filter design problem. It is here called the modified PSO (MPSO) algorithm in which another adjusting factor is more introduced in the velocity updating formula of the algorithm in order to improve the searching ability. In the proposed method, all of the designed filter coefficients are firstly collected to be a parameter vector and this vector is regarded as a particle of the algorithm. The MPSO with a modified velocity formula will force all particles into moving toward the optimal or near optimal solution by minimizing some defined objective function of the optimization problem. To show the effectiveness of the proposed method, two different kinds of linear phase response design examples are illustrated and the general PSO algorithm is compared as well. The obtained results show that the MPSO is superior to the general PSO for the phase response design of digital recursive all-pass filter.

Highlights

An all-pass filter means that its magnitude response is exactly equal to some constant value at all frequencies and independent of frequencies
In [3], an IIR allpass filter with equiripple phase response was designed based on the eigenvalue problem and this design problem can be formulated as the representation of an eigenvalue problem via the Remez exchange algorithm
In the particle swarm optimization (PSO) and modified PSO (MPSO), the variables of the algorithm are given by w = 0.8, c1 = c2 = 0.5, and w = 0.8, c1 = c2 = c3 = 0.5, respectively, for all of the following simulations

Summary

Introduction

An all-pass filter means that its magnitude response is exactly equal to some constant value at all frequencies and independent of frequencies. In [2], for example, the author proposed a new design method for an all-pass filter where it has a least squares or an equiripple phase-error response. It is based on formulating a weighted error between the desired and the actual phase responses in a quadratic form. Unlike the above-mentioned design schemes, this paper attempts to utilize a modified particle optimization (MPSO) algorithm to solve the digital recursive all-pass filter design problem. This developed algorithm is a variant of the general PSO but it has a better searching capacity in solving optimized problems.

Recursive All-Pass Digital Filter

Simulation Results

Conclusions