On the Design of Optimal Digital IIR BP Filter using Opposition aided Cat Swarm Optimization Algorithm

-This paper proposes a solution methodology for the design of optimal and stable digital infinite impulse response (IIR) band pass (BP) filter by employing the cat swarm optimization (CSO) algorithm with the incorporation of oppositional learning strategy. The error surface of digital IIR filters is non linear and multimodal because of the presence of the denominator terms. Therefore, the traditional filter design methods usually got stuck in the local minim. CSO is a novel population based global optimization technique which possesses global as well as local search capabilities. Here, the multicriterion optimization is used as the decisive factor that undertakes the minimization of magnitude approximation error and minimization of ripple magnitudes of pass band and stop band while satisfying the stability constraints that are imposed during the design process. For the purpose of starting with an improved solution set, the opposition based learning strategy is included in CSO. The developed algorithm is used to design the digital IIR band pass (BP) filter and attempts to find the optimal filter coefficients which are approximately close to the desired filter response. The computational results show that the proposed algorithm is capable of designing stable and optimal digital IIR BP filter structure that is better to the designs presented by other algorithms. Keywords--Digital IIR filter, cat swarm optimization algorithm, opposition based learning, filter design, multiparameter optimization. INTRODUCTION The digital filters are generally of two types, finite impulse response (FIR) filters and infinite impulse response (IIR) filters. The digital FIR filter has a finite duration impulse response and its output depends upon the present and past input values only. Hence, these filters are known as non-recursive. On the other hand, the IIR filter has an infinite or continues impulse response and its output depend upon the present and past input values as well as on the previous output values. Hence, they are termed as recursive filters [1, 2]. Over the past few decades, the digital IIR filters have become the target of growing interest as they provide much better performance, improved selectivity and higher computational efficiency than their FIR counterparts for similar magnitude specifications. Also, they have a much sharper roll-offs in their frequency response than the FIR filters of equal complexity. The digital IIR filter designing mainly follows two approaches: (i) transformation approach and (ii) optimization approach. The transformation approach involves the transformation of an analog filter to a digital filter for a given set of prescribed specifications [3]. But the performance of digital IIR filters designed by using the transformation approach is not good as they require too much preknowledge and in most of the cases return a single solution. Also, the designing of digital IIR filter generally faces two problems that are (i) tendency of the filter to become unstable (ii) filter error surface is multimodal in nature due to which conventional design algorithms may stuck at local minima [4, 5]. The stability problem is handled by imposing stability constraints on the filter coefficients. In order to overcome the shortcomings of conventional methods and to achieve a global optimal solution, in the past years many nature inspired optimization algorithms have been implemented for the digital IIR filter design problem. Under the optimization approach various methods like the direct search and the gradient search methods have been proposed. Because of multimodal error surface, the conventional gradient-based algorithm easily stuck at local minima [6]. Therefore, in the past few years numerous nature inspired stochastic optimization technique like the hierarchal genetic algorithm (HGA) [7], hybrid taguchi genetic algorithm (HTGA) [8], taguchi immune algorithm (TIA) [9], real coded genetic algorithm (RCGA) [10], particle swarm optimization (PSO) [11], seeker optimization algorithm (SOA) [12], predator prey optimization (PPO) method [13], heuristic search method (HSM) [14] etc. have been developed and employed for optimal digital IIR filter designing. All these algorithms took the task of digital filter designing and strived hard to obtain structures that are stable and has optimized coefficients. Presently, the development of new and efficient optimization algorithms that use the magnitude approximation error and ripple magnitudes of both pass band and stop band as performance criteria for the designing of optimal digital IIR filters is very much in progress. In this paper, the CSO algorithm is used to design the stable and optimal digital IIR BP filter. CSO is proficient in conducting local as well as global search. Further, an improvement in the form of opposition based learning strategy is used with the purpose of starting International Journal of Engineering Research and General Science Volume 3, Issue 3, May-June, 2015 ISSN 2091-2730 737 www.ijergs.org with better initial solutions by simultaneously checking the opposite solutions. The multicriterion optimization approach is used as the design criterion that undertakes the minimization of magnitude approximation error and minimization of ripple magnitudes of the pass band as well as the stop band while satisfying the stability constraints that are imposed during the design process. The remainder of this paper is organized as follows. Section 2 describes the digital IIR filter designing problem. The details of the mechanism for designing the digital IIR filter using cat swarm optimization algorithm and opposition based learning is described in section 3. Section 4 contains the proposed algorithm steps in detail. In section 5, the performance and statistical analysis of the proposed method has been carried out and the results obtained are compared with the design results in [7], [8], [9], [10] and [14]. Finally, section 6 contains the concluding remarks and scope for future work. PROBLEM STATEMENT The traditional design of digital IIR filter is generally realized by the following difference equation [1]:                M