Design of constrained IIR and interpolated IIR filters using a new semi-definite programming based model reduction technique

This paper proposes a new method for designing IIR filter with peak error constraints and prescribed flatness constraints, such as zeros at stopband. It is based on the model reduction of a FIR function that satisfies the specification by extending a method previously proposed by Brandenstein et al. The proposed model reduction method retains the denominator of the conventional techniques and formulates the optimal design of the numerator as a semi-definite programming problem. Therefore, linear and convex quadratic inequalities such as peak error constraints and prescribed number of zeros at the stopband for the IIR filters can be imposed and solved optimally. Moreover, a method is also proposed to facilitate the efficient implementation of the model reduced IIR filters 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.