AbstractIn this paper, a new Chebyshev approximation (amplitude and phase simulataneous 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 simulataneous 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 compuation can be reduced singnificantly. 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 filtes. It is possible to carry out characteristic approximation limited to the positive frequency range. Hence, a further reduction of the filter order needed for signal processing can be attempted.