Complex Chebyshev approximation to stable IIR filters design

Abstract

This paper presents a minimax design method of stable IIR digital filters with an arbitrary magnitude and phase response using the successive projection (SP) method. Because the design of IIR filters generally results in a complex approximation problem, the complex approximation problem is converted into a real approximation problem and its problem is solved using the SP method. Then, we use the implications of Rouche's theorem to modify the SP method in such a way that a constraint on the maximum pole radius can be incorporated. Hence, the filters obtained can be guaranteed to be stable and are optimum in the Chebyshev sense.