Design of IIR digital filters with prescribed phase error and reduced group-delay error

Digital filters are often required to have constant group delays in many applications. Existing designs of IIR digital filters with no explicit constraints on the filters' group-delay responses usually lead to large group-delay errors, especially near the band edges. In design methods with constraints on group-delay error, much reduction of group-delay error have been obtained, but the phase error may not be small enough. In this paper, we design the IIR filter by imposing constraints on its frequency-response error and phase error, and using a sigmoid upper-bound function to shape the phase error. With this method, we have obtained both small phase error and group-delay error. In order to implement the design method, we combine the Steiglitz-McBride strategy with a relaxation scheme to convert the nonconvex design problem into a series of feasible quadratically constrained quadratic programming problems. Two example filters with specifications given in the literature are provided to compare the proposed design method with several existing methods. Design results demonstrate the effectiveness of the proposed method and good properties of the designed filters.