Universal sampling of band-limited signals

Alexander Olevskii; Alexander Ulanovskii

doi:10.1016/j.crma.2006.04.015

Harmonic Analysis

Universal sampling of band-limited signals

Presented by: Jean-Pierre Kahane

Alexander Olevskii ¹; Alexander Ulanovskii ²

¹ School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
² Stavanger University, NO-4036 Stavanger, Norway

Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 927-931.

Abstract
Résumé

We ask if there exist universal sampling sets of given density, which provide reconstruction or stable reconstruction of every band-limited signal whose spectrum has a small Lebesgue measure. For the stable reconstruction, we show that it is crucial whether the spectrum is compact or dense. On the other hand, the non-stable universal reconstruction is possible in general situation.

Nous posons le problème de l'existence d'ensembles discrets, de densité donnée, permettant par échantillonnage la reconstitution, ou la reconstitution stable, de tout signal dont le spectre a une mesure de Lebesgue assez petite. Pour la reconstitution stable, nous montrons que la réponse dépend de manière cruciale du fait que le spectre soit compact ou soit dense. La reconstitution simple, par contre, est toujours possible.

Received: 2006-03-29
Accepted: 2006-03-30
Published online: 2006-05-22

DOI: 10.1016/j.crma.2006.04.015

Author's affiliations:

Alexander Olevskii ¹; Alexander Ulanovskii ²

¹ School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
² Stavanger University, NO-4036 Stavanger, Norway

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     title = {Universal sampling of band-limited signals},
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Alexander Olevskii; Alexander Ulanovskii. Universal sampling of band-limited signals. Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 927-931. doi : 10.1016/j.crma.2006.04.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.015/

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