An implicit solution for IIR filters with equiripple group delay

This paper presents a method for solving implicitly the poles of recursive digital filters having an equiripple group delay in the given passband. The method applies to low-pass, high-pass, and bandpass filters. The design is based on a transformation mapping the group delay function into another one so that the approximation interval is stretched onto the upper unit semicircle. The equiripple conditions for this new function lead to a system of nonlinear equations in the poles of the filter.