000178427 001__ 178427
000178427 005__ 20190316235420.0
000178427 037__ $$aSTUDENT
000178427 245__ $$aOn localisation and uncertainty measures on graphs
000178427 269__ $$a2012
000178427 260__ $$c2012
000178427 336__ $$aStudent Projects
000178427 520__ $$aDue to the appearance of data on networks such as internet or Facebook, the number of applications of signal on weighted graph is increasing. Unfortunately, because of the irregular structure of this data, classical signal processing techniques are not applicable. In this paper, we examine the windowed graph Fourier transform (WGFT) and propose ambiguity functions to analyze the spread of the window in the vertex-frequency plane. We then observe through examples that there is a trade-off between the vertex and frequency resolution. This matches our intuition form classical signal processing. Finally, we demonstrate an uncertainty principle for the spread of the ambiguity function. We verify with examples that this principle is sharp for the extreme values of and emphasize the difference between the generalized graph ambiguity function and the classical one. We finish with demonstration of some Young and Hausdorff-Young like inequalities for graphs.
000178427 6531_ $$alocalisation, uncertainty, graph, network, windowed Fourier transform, ambiguity function, convolution, inequalities
000178427 700__ $$0247306$$g179669$$aPerraudin, Nathanaël
000178427 720_2 $$aVandergheynst, Pierre$$edir.$$g120906$$0240428
000178427 720_2 $$aShuman, David$$edir.$$g201233$$0242930
000178427 8564_ $$uhttps://infoscience.epfl.ch/record/178427/files/report.pdf$$zn/a$$s2262421$$yn/a
000178427 909C0 $$xU10380$$0252392$$pLTS2
000178427 909CO $$qGLOBAL_SET$$pSTI$$ooai:infoscience.tind.io:178427
000178427 917Z8 $$x179669
000178427 937__ $$aEPFL-STUDENT-178427
000178427 973__ $$sPUBLISHED$$aEPFL
000178427 980__ $$bMASTERS$$aSTUDENT