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Computational Intelligence and Neuroscience
Volume 2015 (2015), Article ID 638068, 7 pages
Research Article

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

Department of Computer and Communication, Shu-Te University, Kaohsiung 824, Taiwan

Received 5 October 2014; Revised 22 December 2014; Accepted 1 January 2015

Academic Editor: Rahib H. Abiyev

Copyright © 2015 Wei-Der Chang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.