Minimax design of IIR digital filters with reduced group-delay error

Existing minimax design methods of infinite impulse response digital filters with no constraints on the filters´ group-delay usually lead to large group-delay errors, especially near the band edges. Much reduction of group-error may be obtained in designs with constraints on group-delay error, but the phase error may be large. In this paper, the right-sided sigmoid upper-bound functions is introduced to shape the phase error of low-pass IIR digital filters to obtain a minimax design with specified phase error upper-bound. The large group-delay error near the band edges can be effectively suppressed by this method. A sequential constrained least-squares method is used to solve the constrained minimax design in this paper, and the Levy-Sanathanan-Koerner strategy is used to convert the nonconvex least-square subproblems into convex ones. Design examples demonstrate the effectiveness of the proposed method.