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FIR (finite impulse response) digital filter design is a fundamental problemin signal processing. In particular, FIR approximation of analog filters (orsystems) is ubiquitous not only in signal processing but also in digitalimplementation of controllers. In this article, we propose a new design methodof an FIR digital filter that optimally approximates a given analog filter inthe 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, wereduce the H-infinity optimization to a convex optimization described by an LMI(linear matrix inequality). We also extend the method to multi-rate andmulti-delay systems. A design example is shown to illustrate the effectivenessof the proposed method.

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