A Windowed Digraph Fourier Transform
Rasoul Shafipour, Ali Khodabakhsh, Gonzalo Mateos
Abstract
We propose a methodology to carry out vertex-frequency analyses of graph signals, with the goal of unveiling the signal's frequency occupancy over a localized region in the network. To this end, we first introduce localized graph signals in the vertex domain, by defining windows that are localized around each node by construction. Recent directed graph Fourier transform (DGFT) advances facilitate the frequency analysis of said localized signals, to reveal the signal's energy distribution in a way akin to a spectrogram in the vertex-frequency plane. We then learn a set of windows by applying gradient descent method to an optimization problem governed by penalty parameters in the spectral domain. We also argue about the tradeoff between the resolution in the vertex and frequency domains based on the said parameters. We evaluate the performance of the proposed windowed GFT approach through numerical experiments on synthetic and real-world graphs.
BibTeX
@inproceedings{icassp2019_awindoweddigraph,
title = {A Windowed Digraph Fourier Transform},
author = {Rasoul Shafipour and Ali Khodabakhsh and Gonzalo Mateos},
booktitle = {ICASSP 2019},
year = {2019}
}