Research Article Two-Dimensional IIR Filter Design Using Simulated Annealing Based Particle Swarm Optimization Supriya Dhabal 1 and Palaniandavar Venkateswaran 2 1 Department of Electronics and Communication Engineering, Netaji Subhash Engineering College, Garia, Kolkata, West Bengal 700152, India 2 Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata, West Bengal 700032, India Correspondence should be addressed to Supriya Dhabal; supriya dhabal@yahoo.co.in Received 14 May 2014; Revised 16 August 2014; Accepted 23 August 2014; Published 9 September 2014 Academic Editor: Ling Wang Copyright © 2014 S. Dhabal and P. Venkateswaran. Tis 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. We present a novel hybrid algorithm based on particle swarm optimization (PSO) and simulated annealing (SA) for the design of two-dimensional recursive digital flters. Te proposed method, known as SA-PSO, integrates the global search ability of PSO with the local search ability of SA and ofsets the weakness of each other. Te acceptance criterion of Metropolis is included in the basic algorithm of PSO to increase the swarm’s diversity by accepting sometimes weaker solutions also. Te experimental results reveal that the performance of the optimal flter designed by the proposed SA-PSO method is improved. Further, the convergence behavior as well as optimization accuracy of proposed method has been improved signifcantly and computational time is also reduced. In addition, the proposed SA-PSO method also produces the best optimal solution with lower mean and variance which indicates that the algorithm can be used more efciently in realizing two-dimensional digital flters. 1. Introduction Design of two-dimensional (2D) flters has been considered extensively over the past two decades as it plays a very sig- nifcant role in the domain of biomedical image processing, satellite imaging, seismic data processing, and so forth [1]. It is well known that digital flters are typically classifed into two groups: recursive or infnite impulse response (IIR) and nonrecursive or fnite impulse response (FIR) flters. Design of IIR flters has received much more attention, because IIR flters can provide a better performance than FIR flters, having the same number of flter coefcients. But the main problems of IIR flters are that they have a multimodal error surface and they may also be unstable in some cases. To overcome the problem of multimodal error surface, a global optimization method can be adopted more efciently. Te stability problem can be tackled by limiting the problem space as appropriate constraints from the beginning of optimization routine [1, 2]. Similar to 1D flter, 2D IIR flters can also meet the same desired specifcations with less number of coefcients than required for an equivalent 2D FIR flter. Te design methodology for 2D flters grouped in two ways: McClellan transformation based design of 2D flters from 1D prototype and another one based on appropriate optimization techniques [1–6]. In optimization based methods, the design problem can be formulated as a constrained minimization problem and they are solved by various global optimization techniques. Previously reported work on this problem has applied diferent optimization techniques, like neural network (NN) [1], genetic algorithm (GA) [2], computer language GENETICA [3], Taguchi-based immune algorithm [4], Bees algorithm [5], and particle swarm optimization (PSO) [6], efciently. Most of these algorithms exhibit slow convergence to achieve a good near- optimum solution and are easily trapped into local optima. Tese shortcomings can be avoided by introducing SA with PSO because the frst one has strong local exploration capabilities and PSO exhibits fast global searching abilities. Earlier reported works demonstrated that by combining SA with PSO, signifcant improvements are achieved for Hindawi Publishing Corporation Journal of Optimization Volume 2014, Article ID 239721, 10 pages http://dx.doi.org/10.1155/2014/239721