Enhanced Steiglitz-McBride Procedure for Minimax IIR Digital Filters

This paper presents an enhanced Steiglitz-McBride (SM) procedure for the design of stable minimax IIR digital filters. It is well known that minimax design of IIR filters is typically initiated with a nonconvex formulation, followed by a procedure to relax the original design problem to a sequence of convex sub-problems to be solved iteratively. We proposed an enhanced SM procedure that leads to improved convex relaxation relative to the conventional SM techniques, hence to improved designs. In addition, we make an observation that the state-of-the-art convex stability constraint based on strictly positive realness is equivalent to that deduced from an enhanced version of Rouché theorem from complex analysis. Design examples are presented to evaluate the new design algorithm.