FIR Digital Filter Design by Sampled-Data H-infinity Discretization

FIR (finite impulse response) digital filter design is a fundamental problem in signal processing. In particular, FIR approximation of analog filters (or systems) is ubiquitous not only in signal processing but also in digital implementation of controllers. In this article, we propose a new design method of an FIR digital filter that optimally approximates a given analog filter in the sense of minimizing the H-infinity norm of the sampled-data error system. By using the lifting technique and the KYP (Kalman-Yakubovich-Popov) lemma, we reduce the H-infinity optimization to a convex optimization described by an LMI (linear matrix inequality). We also extend the method to multi-rate and multi-delay systems. A design example is shown to illustrate the effectiveness of the proposed method.