2-Dimensional Finite Impulse Response Graph-Temporal Filters

TL;DR

This paper introduces 2D FIR graph-temporal filters that effectively capture both spatial and temporal variations in time-varying graph signals, enabling distributed implementation and analysis of stochastic signals.

Contribution

It extends FIR graph filters to jointly process graph and temporal data, providing a novel 2D filter design and analysis framework for time-varying signals.

Findings

Separable graph-temporal filters can be implemented in a distributed manner.

The approach accurately characterizes moments of stochastic graph signals.

Filter design can be performed independently in graph and time domains.

Abstract

Finite impulse response (FIR) graph filters play a crucial role in the field of signal processing on graphs. However, when the graph signal is time-varying, the state of the art FIR graph filters do not capture the time variations of the input signal. In this work, we propose an extension of FIR graph filters to capture also the signal variations over time. By considering also the past values of the graph signal, the proposed FIR graph filter extends naturally to a 2-dimensional filter, capturing jointly the signal variations over the graph and time. As a particular case of interest we focus on 2-dimensional separable graph-temporal filters, which can be implemented in a distributed fashion at the price of higher communication costs. This allows us to give filter specifications and perform the design independently in the graph and temporal domain. The work is concluded by analyzing the proposed approach for stochastic graph signals, where the first and second order moments of the output signal are characterized.