Digital Signal Processing 18 (2008) 657–668 www.elsevier.com/locate/dsp Linear phase FIR filter design using particle swarm optimization and genetic algorithms Jehad I. Ababneh a,∗ , Mohammad H. Bataineh b a Department of Electrical Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan b Department of Communication, Hijjawi Faculty for Engineering Technology, Yarmouk University,Irbid, Jordan Available online 27 June 2007 Abstract In this paper, a linear phase FIR filter is designed using particle swarm optimization (PSO) and genetic algorithms (GA). Two de- sign cases are considered. In the first case, the filter length, passband and stopband frequencies, and the ratio of the passband and stopband ripples size are specified. In the second case, a feasible passband and stopband ripples size in addition to the other three filter specifications are specified. The later situation is not explicitly considered by the Parks–McClellan (PM) algorithm. Further- more, the PSO and the GA are used to design optimum FIR filters for which the filter coefficients are represented using finite word length. In all cases, the design goal is successfully achieved using the PSO and compared with that obtained using the GA. For the problem at hand, it is found that the PSO outperforms the GA in some of the presented design cases.  2007 Elsevier Inc. All rights reserved. Keywords: FIR filters; Digital filters design; Particle swarm optimization; Parks–McClellan algorithm 1. Introduction The simplest design of FIR filters is achieved using the windowing method. In this method, the design starts with an ideal desired frequency response given by H d (e jw ) = ∞  n=−∞ h d [n]e −jwn , (1) where h d [n] represents the impulse response of the ideal filter. Then, a causal FIR approximation can be obtained from h d [n] by two steps. First, h d [n] is multiplied by a finite length sequence d [n] (window) to obtain a finite length impulse response. Second, causality is introduced by time delaying the windowed impulse response. In mathematical terms h w [n]= h d [n]d [n], (2) * Corresponding author. Fax: +962 27095 018. E-mail address: ababnehj@just.edu.jo (J.I. Ababneh). 1051-2004/$ – see front matter  2007 Elsevier Inc. All rights reserved. doi:10.1016/j.dsp.2007.05.011