Design of Constrained Causal Stable IIR Filters Using a New Second- Order-Cone-Programming-Based Model-Reduction Technique

This brief proposes a new method for designing infinite-impulse response (IIR) filter with peak error and prescribed flatness constraints. It is based on the model reduction of a finite-impulse response function that satisfies the specification by extending a method previously proposed by Brandenstein. The proposed model-reduction method retains the denominator of the conventional techniques and formulates the optimal design of the numerator as a second-order cone programming problem. Therefore, linear and convex quadratic inequalities such as peak error constraints and prescribed number of zeros at the stopband for IIR filters can be imposed and solved optimally. Moreover, a method is proposed to express the denominator of the model-reduced IIR filter as a polynomial in integer power of z, which efficiently facilitates its polyphase implementation in multirate applications. Design examples show that the proposed method gives better performance, and more flexibility in incorporating a wide variety of constraints than conventional methods