Distributed Autoregressive Moving Average Graph Filters

TL;DR

This paper introduces a novel class of ARMA graph filters that can be implemented in a distributed manner, offering robustness to graph and signal variations, and unifying graph and time domain filtering.

Contribution

It presents the design of ARMA graph filters that are independent of specific graphs and demonstrates their robustness and dual domain behavior.

Findings

ARMA graph filters can be implemented in a distributed fashion.

They are robust against changes in signals and graphs.

They behave as ARMA filters in both graph and time domains.

Abstract

We introduce the concept of autoregressive moving average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finite-impulse response (FIR) graph filters, ARMA graph filters are robust against changes in the signal and/or graph. In addition, when time-varying signals are considered, we prove that the proposed graph filters behave as ARMA filters in the graph domain and, depending on the implementation, as first or higher ARMA filters in the time domain.