Minimax design of IIR digital filters with near-uniform group delay error

Digital filters are often required to have constant group delays in many applications. Though some existing designs of IIR digital filters have obtained both small magnitude error and phase error, they often lead to large group-delay error, especially near the band edges. In this paper, we design the IIR filter by imposing two elliptical constraints respectively on magnitude error and phase error and using a modified envelope of the group-delay error to shape the phase error. With this method, we have obtained comparably small phase error and greatly reduced group-delay error. The resulting optimization problem is a nonconvex one, we propose to use the Levy-Sanathanan-Koerner strategy and a sequential constrained least-squares method to convert the nonconvex problem into a sequence of easily solvable convex problems. Design examples demonstrate the effectiveness of the proposed method.