Minimax Phase Error Design of Stable IIR Filters Using a Sequential Minimization Method

For the design of IIR digital filters, one challenge is their inherent non-linear phase responses. The double-ellipse model controls the phase error and magnitude error separately and is a good candidate for near linear-phase IIR filter design. Another challenge is their stability conditions. The stability-triangle condition defines a necessary and sufficient stability domain of an IIR filter, and thus is much preferable in the design of IIR filters. This paper incorporates the stability-triangle conditions with the double-ellipse model, and then applies a sequential minimization method to solve the magnitude constrained minimax phase error design of IIR filters. Design examples demonstrate that the proposed method has obtained better filters with smaller phase error than existing algorithms.