Design of linear-phase digital FIR filter using Differential Evolution optimization with ripple constraint

For the optimal design of frequency-selective digital filters, evolutionary optimization algorithms have been applied. In these design methods the desired filter´s frequency characteristics are specified in terms of its frequency response. The goal of the optimization process is to find the optimal filter coefficients which closely approximate the desired frequency response. In this paper, Differential Evolution (DE) algorithm is described for the design of digital FIR filter with ripple constraint. The proposed algorithm minimizes ripples, using a constraint handling method based on penalty function. The results for the case of DE algorithm with ripple constraint are compared with those obtained for the same algorithm without ripple constraint. A ripple constraint has ensured that the maximum error magnitude between desired frequency response and the designed frequency response is equal to or below the constraint in the specified frequency band. The results show the reduction in the size of stopband ripple when DE algorithm with ripple constraint handling approach is applied. The performance obtained using this approach is comparable with that of Least-square design method for FIR filters when number of runs is applied.