Design of Infinite Impulse Response Filter Using Fractional Derivative Constraints and Hybrid Particle Swarm Optimization

Abstract

In this paper, a new method for designing digital infinite impulse response filter with nearly linear-phase response is presented using fractional derivative constraints (FDC). The design problem is constructed as a phase optimization problem between the desired and designed phase response of a filter. In order to achieve the highly accurate passband (pb) response, phase response is fitted to desired response more precisely using FDC, due to which design problem becomes a multimodal error surface that is constructed from sum of passband error (ep) and stopband error (es). Optimal value of FDC is accomplished by minimizing the total error (er0) using improved swarm-based optimization technique, which is formulated by associating the scout bee mechanism of artificial bee colony algorithm with particle swarm optimization and termed as hybrid particle swarm optimization. The simulated results reflect that the improved response in passband along with better transition width is achieved using the proposed method. It is observed that about 90–99% of improvement in passband error can be achieved with 100% reduction in maximum passband ripple. However, slight reduction in stopband attenuation (As), in some cases, results within the permissible limit. The designed filters using this method are also stable toward finite word length effect.