Average sampling in $ {L}^{2}$

Nashed, M. Zuhair; Sun, Qiyu; Tang, Wai-Shing

doi:10.1016/j.crma.2009.07.011

Mathematical Analysis/Theory of Signals

Average sampling in

L^{2}

[Échantillonnage moyenne dans

L^{2}

]

Présenté par : Yves Meyer

Nashed, M. Zuhair ¹ ; Sun, Qiyu ¹ ; Tang, Wai-Shing ²

¹ Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
² Department of Mathematics, National University of Singapore, Singapore

Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 1007-1010.

Résumé
Abstract

Dans cette Note, nous démontrons que tout échantillonneur moyen localisé ne peut pas être un échantillonneur stable pour $L^{2}$ , mais qu'un échantillonneur déterminant localisé existe pour $L^{2}$ .

In this Note, we show that any localized average sampler could not be a stable sampler for $L^{2}$ , but that there is a localized determining sampler for $L^{2}$ .

Reçu le : 2009-01-14
Accepté le : 2009-07-06
Publié le : 2009-08-06

DOI : 10.1016/j.crma.2009.07.011

Affiliations des auteurs :

Nashed, M. Zuhair ¹ ; Sun, Qiyu ¹ ; Tang, Wai-Shing ²

¹ Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
² Department of Mathematics, National University of Singapore, Singapore

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Nashed, M. Zuhair; Sun, Qiyu; Tang, Wai-Shing. Average sampling in $ {L}^{2}$. Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 1007-1010. doi : 10.1016/j.crma.2009.07.011. http://archive.numdam.org/articles/10.1016/j.crma.2009.07.011/

Bibliographie
Cité par

[1] Aldroubi, A. Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces, Appl. Comput. Harmon. Anal., Volume 13 (2002), pp. 151-161

[2] Aldroubi, A.; Gröchenig, K. Nonuniform sampling and reconstruction in shift-invariant space, SIAM Rev., Volume 43 (2001), pp. 585-620

[3] Aldroubi, A.; Sun, Q.; Tang, W.-S. Convolution, average sampling and a Calderon resolution of the identity for shift-invariant spaces, J. Fourier Anal. Appl., Volume 11 (2005), pp. 215-244

[4] Bi, N.; Nashed, M.Z.; Sun, Q. Reconstructing signals with finite rate of innovation from noisy samples, Acta Appl. Math., Volume 107 (2009), pp. 339-372

[5] Koosis, P. Sur la totalite des systemes d'exponentielles imaginaries, C. R. Acad. Sci. Paris, Volume 250 (1960), pp. 2102-2103

[6] Sun, Q. Non-uniform average sampling and reconstruction of signals with finite rate of innovation, SIAM J. Math. Anal., Volume 38 (2006), pp. 1389-1422

[7] Vetterli, M.; Marziliano, P.; Blu, T. Sampling signals with finite rate of innovation, IEEE Trans. Signal Process., Volume 50 (2002), pp. 1417-1428

[8] Unser, M. Sampling – 50 years after Shannon, Proc. IEEE, Volume 88 (2000), pp. 569-587

[9] Unser, M.; Aldroubi, A. A general sampling theory for non-ideal acquisition devices, IEEE Trans. Signal Process., Volume 42 (1994), pp. 2915-2925

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