Comptes Rendus
no. 17-18
Mathematical Analysis/Theory of Signals
Average sampling in L2
[Échantillonnage moyenne dans L2]

Présenté par : Yves Meyer

M. Zuhair Nashed1 ; Qiyu Sun1 ; Wai-Shing Tang2
1 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
2 Department of Mathematics, National University of Singapore, Singapore
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1007-1010.

Dans cette Note, nous démontrons que tout échantillonneur moyen localisé ne peut pas être un échantillonneur stable pour L2, mais qu'un échantillonneur déterminant localisé existe pour L2.

In this Note, we show that any localized average sampler could not be a stable sampler for L2, but that there is a localized determining sampler for L2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.07.011
M. Zuhair Nashed 1 ; Qiyu Sun 1 ; Wai-Shing Tang 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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M. Zuhair Nashed; Qiyu Sun; Wai-Shing Tang. Average sampling in $ {L}^{2}$. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1007-1010. doi : 10.1016/j.crma.2009.07.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.07.011/

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

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

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

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

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

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

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

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

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