On the degrees of freedom of signals on graphs

descriptionPublicationkeyboard_double_arrow_right Article , Conference object , Preprint 01 Aug 2015Embargo end date: 01 Dec 2015 Italy Publisher:IEEEJournal:2015 23rd European Signal Processing Conference (EUSIPCO)Funded by:EC | TROPIC

Authors: MIkhail Tsitsvero; Sergio Barbarossa;

doi: 10.1109/eusipco.2015.7362635 , 10.48550/arxiv.1512.00783 , 10.5281/zenodo.38847

arXiv: 1512.00783

handle: 11573/1164827

On the degrees of freedom of signals on graphs

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Abstract

Continuous-time signals are well known for not being perfectly localized in both time and frequency domains. Conversely, a signal defined over the vertices of a graph can be perfectly localized in both vertex and frequency domains. We derive the conditions ensuring the validity of this property and then, building on this theory, we provide the conditions for perfect reconstruction of a graph signal from its samples. Next, we provide a finite step algorithm for the reconstruction of a band-limited signal from its samples and then we show the effect of sampling a non perfectly band-limited signal and show how to select the bandwidth that minimizes the mean square reconstruction error.

5 pages, 2 figures; Presented on 23-rd European Signal Processing Conference (EUSIPCO), September, 2015, Nice, France

Country

Italy

Related Organizations

Roma Tre University
Italy
Sapienza University of Rome
Italy

Keywords

FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Computer Science - Information Theory, Information Theory (cs.IT), graph fourier transform; graph signal recovery; sampling on graph; media technology; 1707; signal processing, Computer Science - Discrete Mathematics

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