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

TL;DR

This paper introduces a novel FIR digital filter design method that optimally approximates analog filters by minimizing the H-infinity norm of the error, using convex optimization techniques.

Contribution

It presents a new approach combining lifting, KYP lemma, and LMI to design FIR filters with optimal H-infinity approximation of analog filters, including multi-rate and multi-delay systems.

Findings

Effective FIR approximation of analog filters demonstrated

Convex optimization approach reduces design complexity

Method extends to multi-rate and multi-delay systems

Abstract

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.