Complex Chebyshev approximation for infinite impulse response digital filters

In this paper, a new Chebyshev approximation (amplitude and phase simultaneous approximation) method for IIR digital filters is proposed. The proposed algorithm is based on the Remez algorithm. By solving the eigenvalue problem at each iteration, the frequency characteristic of the filter is interpolated so that the error function in the complex domain is made with equal ripples. Since the previously proposed amplitude and phase simultaneous approximation methods for the IIR digital filters are based on the nonlinear equation, they all require substantial computation. On the other hand, the present method is extremely simple and the amount of computation can be reduced significantly. Nevertheless, the performance equal to or more than the conventional one can be obtained. Further, the present method can be applied not only for the real coefficient filters but also for the complex coefficient filters. It is possible to carry out characteristic approximations limited to the positive frequency range. Hence, a further reduction of the filter order needed for signal processing can be attempted.