Shuman, David
Ricaud, Benjamin
Vandergheynst, Pierre
A Windowed Graph Fourier Transform
2012 Ieee Statistical Signal Processing Workshop (Ssp)
978-1-4673-0183-1
133-136
4
The prevalence of signals on weighted graphs is increasing; however, because of the irregular structure of weighted graphs, classical signal processing techniques cannot be directly applied to signals on graphs. In this paper, we define generalized translation and modulation operators for signals on graphs, and use these operators to adapt the classical windowed Fourier transform to the graph setting, enabling vertex-frequency analysis. When we apply this transform to a signal with frequency components that vary along a path graph, the resulting spectrogram matches our intuition from classical discrete-time signal processing. Yet, our construction is fully generalized and can be applied to analyze signals on any undirected, connected, weighted graph.
Signal processing on graphs;
Time-frequency analysis;
Generalized translation and modulation;
Spectral graph theory;
Ieee
New York
2012
http://infoscience.epfl.ch/record/175341/files/WGFT_SSP_2012.pdf;