This paper focuses on the design of IIR digital filters with the specified magnitude and group delay responses using differential evolution (DE). In the IIR filter design problems using DE, the parameters to be optimized are the poles and zeros of transfer functions. Therefore, the stability of the obtained filter can easily be guaranteed. Moreover, the proposed method can directly specify not only the maximum magnitude deviation in the pass- and stop-bands but also the maximum allowable peak in the transition-band. In the design examples, we show the relationships between the maximum allowable peak in the transition-band and the stop-band attenuation, and clarify the effectiveness of the proposed method.
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