[Échantillonnage universel de signaux à spectre borné]
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.
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.
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@article{CRMATH_2006__342_12_927_0,
author = {Olevskii, Alexander and Ulanovskii, Alexander},
title = {Universal sampling of band-limited signals},
journal = {Comptes Rendus. Math\'ematique},
pages = {927--931},
publisher = {Elsevier},
volume = {342},
number = {12},
year = {2006},
doi = {10.1016/j.crma.2006.04.015},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2006.04.015/}
}
TY - JOUR AU - Olevskii, Alexander AU - Ulanovskii, Alexander TI - Universal sampling of band-limited signals JO - Comptes Rendus. Mathématique PY - 2006 SP - 927 EP - 931 VL - 342 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2006.04.015/ DO - 10.1016/j.crma.2006.04.015 LA - en ID - CRMATH_2006__342_12_927_0 ER -
%0 Journal Article %A Olevskii, Alexander %A Ulanovskii, Alexander %T Universal sampling of band-limited signals %J Comptes Rendus. Mathématique %D 2006 %P 927-931 %V 342 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2006.04.015/ %R 10.1016/j.crma.2006.04.015 %G en %F CRMATH_2006__342_12_927_0
Olevskii, Alexander; Ulanovskii, Alexander. Universal sampling of band-limited signals. Comptes Rendus. Mathématique, Tome 342 (2006) no. 12, pp. 927-931. doi : 10.1016/j.crma.2006.04.015. http://archive.numdam.org/articles/10.1016/j.crma.2006.04.015/
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