A Sequential Partial Optimization Algorithm for Minimax Design of Separable-Denominator 2-D IIR Filters

A sequential partial optimization method is presented in this paper for the minimax design of two-dimensional infinite impulse response filters with separable denominator. The method converts the minimax design problem into a sequence of smaller subproblems, each updating only one pair of second-order denominator factors. The necessary and sufficient stability triangles for one-dimensional filters are used as the stability constraints on the two-dimensional filters. The first-order Taylor expansion and a trust-region method are used to deal with the nonconvexity of the subproblems and guarantee the convergence of the solution algorithm. By comparing with a corresponding joint optimization method, the sequential partial optimization algorithm is shown to converge faster for filters with relatively high denominator order. This is mainly due to the observation that the trust region to assure the convergence is usually much smaller for the joint optimization method. Moreover, the limit solution of the sequential partial optimization algorithm has been proved to be a Karush-Kuhn-Tucker point of the design problem. Design examples demonstrate that the proposed algorithm has obtained smaller maximum frequency response errors than the competing methods both for filters with separable denominator of the same order and for filters with nonseparable denominator of about the same implementation complexity.