Design of Optimal Digital IIR Filters by Using an Improved Immune Algorithm

In this paper, based on both the features of a biological immune system and the systematic reasoning ability of the Taguchi method, an improved immune algorithm, named the Taguchi-immune algorithm (TIA), is proposed to solve the problem of designing the optimal digital infinite impulse response (IIR) filters. In the TIA, the clonal proliferation within hypermutation for several antibody diversifications and the recombination by using the Taguchi method for the local search are integrated to improve the capabilities of exploration and exploitation. The systematic reasoning ability of the Taguchi method is executed in the recombination operations to select the better antibody genes to achieve the potential recombination, and consequently enhance the TIA. Based on minimizing the L
_p
-norm approximation error and minimizing the ripple magnitudes of both passband and stopband, a multicriterion combination is employed as the design criterion to obtain the optimal IIR filter that can fit different performance requirements. The proposed TIA approach is effectively applied to solve the multiparameter and multicriterion optimization problems of designing the digital low-pass, high-pass, bandpass, and bandstop filters. In these studied problems, there are many parameters and numerous local optima so that these studied problems are challenging enough for evaluating the performances of any proposed evolutionary approaches. The computational experiments show that the proposed TIA approach can obtain better digital IIR filters than the existing methods such as the genetic-algorithms-based method and the classic methods