Digital stable IIR low pass filter optimization using PSO-CFIWA

In this paper, an optimal design of stable digital low pass infinite impulse response (IIR) filter using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSO-CFIWA) has been presented. In the design process, the filter length, pass band and stop band frequencies, feasible pass band and stop band ripple sizes are specified. IIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for digital IIR filter design due to the sub-optimality problem. Given the filter specifications to be realized, the PSO-CFIWA algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency response characteristic. In this paper, for the given problem, the design of the optimal IIR low pass filter of order eight has been performed. The simulation results have been compared to those obtained by the well accepted evolutionary algorithms such as particle swarm optimization (PSO), real coded genetic algorithm (RGA). The results justify that the proposed optimal filter design approach using PSO-CFIWA outperforms RGA and PSO, not only in the accuracy of the designed filter but also in the convergence speed and solution quality i.e. the stop band attenuation. Further, the pole zero analysis justifies the stability of the designed optimized IIR filter.