Hybrid method for designing digital FIR filters based on fractional derivative constraints

Abstract

In this manuscript, a hybrid approach based on Lagrange multiplier method and cuckoo search (CS) optimization technique is proposed for the design of linear phase finite impulse response (FIR) filters using fractional derivative constraints. In the proposed method, FIR filter is designed by optimizing the integral squares in passband and stopband from ideal response such that the fractional derivatives of designed filter response become zero at a given frequency point. Lagrange multiplier method is exploited for finding the optimized filter coefficients. Optimal value of fractional derivative constraints for optimized filter coefficients are determined by minimizing the objective function constructed using a sum of maximum passband ripple and maximum stopband ripple in frequency domain using CS algorithm. Performance of the proposed method is evaluated by passband error (ϕp), stopband error (ϕs), stopband attenuation (As), maximum passband ripple (MPR), maximum stopband ripple (MSR) and CPU time. A comparative study of the performance of particle swarm optimization (PSO) and artificial bee colony (ABC) for designing FIR filters using the proposed method is also made.