Min-Max Design of FIR Digital Filters by Semidefinite Programming

TL;DR

This paper introduces a semidefinite programming approach for FIR filter design, including approximation of IIR filters and inverse filtering, utilizing KYP lemma and LMIs, with MATLAB implementations and an illustrative example.

Contribution

It presents a novel semidefinite programming framework for FIR filter design based on KYP lemma, enabling efficient solutions for approximation and inverse filtering problems.

Findings

Effective FIR approximation of IIR filters demonstrated.

Inverse FIR filtering of FIR and IIR filters achieved.

MATLAB codes validate the proposed methods.

Abstract

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.