WLS Design of ARMA Graph Filters using Iterative Second-Order Cone Programming

TL;DR

This paper introduces a novel weighted least-squares approach for designing ARMA graph filters, utilizing iterative second-order cone programming to enhance frequency response accuracy and stability.

Contribution

It presents a new WLS design method for ARMA graph filters that reformulates the problem into a stable, iterative second-order cone programming framework.

Findings

Improved frequency response of ARMA graph filters

Enhanced stability in filter design

Outperforms previous WLS methods in experiments

Abstract

We propose a weighted least-square (WLS) method to design autoregressive moving average (ARMA) graph filters. We first express the WLS design problem as a numerically-stable optimization problem using Chebyshev polynomial bases. We then formulate the optimization problem with a nonconvex objective function and linear constraints for stability. We employ a relaxation technique and convert the nonconvex optimization problem into an iterative second-order cone programming problem. Experimental results confirm that ARMA graph filters designed using the proposed WLS method have significantly improved frequency responses compared to those designed using previously proposed WLS design methods.