A Sequential Minimization Procedure for Minimax Design of IIR Filters Based on Second-Order Factor Updates

In order to make good use of the linearity, necessity, and sufficiency of the stability-triangle-based stability conditions, a sequential minimization procedure is proposed in this brief to convert the minimax design of an infinite impulse response (IIR) filter to a sequence of minimax subproblems. Aside from the numerator, only one second-order factor of the denominator is optimized in each of the minimax subproblems. The sequential minimization procedure is then combined with a Levy-Sanathanan-Koerner-based direct minimization method for the subproblems. Many IIR filters have been designed using the proposed procedure. Three examples are provided for a comparison of the procedure with some recent design methods. Design results show that the proposed procedure has obtained much better minimax filters.