Min-Max Design of FIR Digital Filters by Semidefinite Programming

In this article we consider two problems: FIR (Finite Impulse Response) approximation of IIR (Infinite Impulse Response) filters and inverse FIR filtering of FIR or IIR filters. By means of Kalman-Yakubovich-Popov (KYP) lemma and its generalization (GKYP), the problems are reduced to semidefinite programming described in linear matrix inequalities (LMIs). MATLAB codes for these design methods are given. An design example shows the effectiveness of these methods.