A New Design Method for Stable IIR Filters With Nearly Linear-Phase Response Based on Fractional Derivative and Swarm Intelligence

摘要

In this paper, a new design method based on fractional derivative (FD) is proposed for designing digital stable infinite impulse response (IIR) filters with nearly linear-phase response. In this method, the design problem is formulated as a phase error optimization of an all-pass filter connected in parallel with a pure delay function. FD is employed to improve the frequency response of the filter at some reference point (ω₀) in the passband. Optimal values of FD constraints and reference points in passband are determined by minimizing the sum of error in passband (E_p) and stopband (E_s) of an IIR filter, using different evolutionary techniques such as particle swarm optimization (PSO), constraint factor inertia PSO (CFI-PSO), quantum PSO, artificial bee colony algorithm, and cuckoo search technique. Comparative study provides evidence that the proposed method, based on CFI-PSO, gives the best performance amongst the employed swarm-based techniques. Experimental results show the impact of the proposed method as compared to earlier reported techniques in terms of improved response in passband and sharper transition width. However, small reduction in stopband attenuation (A_s) is observed within the allowable limit when compared to nonfractional design approaches.