Multi-criterion satisfactory optimization method for designing IIR digital filters

This paper proposes a novel method called multi-criterion satisfactory optimization method (MCSOM) to design infinite impulse response (IIR) filters. The core of the method is that multiple criteria can be adjusted conveniently, according to different requirements of different designers for performances of pass bands, stop bands and transition bands of IIR digital filters. The method can be employed directly in frequency domain. By designing performance specification satisfaction rate functions and synthesis satisfactory rate function of IIR digital filters, satisfactory optimization model is constructed. The model is characterized by considering satisfactory design of performance specifications and optimization of parameters of IIR digital filters, simultaneously. Furthermore, a new quantum genetic algorithm (NQGA) is also proposed to search automatically satisfactory solution in IIR digital filter design in this paper. Rapid convergence and good global search capability characterized the performance of NQGA. The effectiveness, applicability and flexibility of MCSOM based on NQGA are demonstrated by experimental results on the lowpass and bandpass IIR digital filters design. The results show that the introduced method is superior to Yule-Walker method and the method in Li Jianhua and Yin Fuliang (1996).