TY - CPAPER
AB - 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.
T1 - A Windowed Graph Fourier Transform
DA - 2012
AU - Shuman, David
AU - Ricaud, Benjamin
AU - Vandergheynst, Pierre
JF - 2012 Ieee Statistical Signal Processing Workshop (Ssp)
SP - 133-136
EP - 133-136
PB - Ieee
PP - New York
ID - 175341
KW - Signal processing on graphs
KW - Time-frequency analysis
KW - Generalized translation and modulation
KW - Spectral graph theory
SN - 978-1-4673-0183-1
UR - http://infoscience.epfl.ch/record/175341/files/WGFT_SSP_2012.pdf
ER -