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

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

doi:10.1016/j.crma.2009.07.011

Mathematical Analysis/Theory of Signals

Average sampling in

L^{2}

Presented by: Yves Meyer

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

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

Abstract (Original language)
Résumé

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 $L^{2}$ .

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 $L^{2}$ .

Received: 2009-01-14
Accepted: 2009-07-06
Published online: 2009-08-06

DOI: 10.1016/j.crma.2009.07.011

Author's affiliations:

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

@article{CRMATH_2009__347_17-18_1007_0,
     author = {M. Zuhair Nashed and Qiyu Sun and Wai-Shing Tang},
     title = {Average sampling in $ {L}^{2}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1007--1010},
     year = {2009},
     publisher = {Elsevier},
     volume = {347},
     number = {17-18},
     doi = {10.1016/j.crma.2009.07.011},
     language = {en},
}

TY  - JOUR
AU  - M. Zuhair Nashed
AU  - Qiyu Sun
AU  - Wai-Shing Tang
TI  - Average sampling in $ {L}^{2}$
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 1007
EP  - 1010
VL  - 347
IS  - 17-18
PB  - Elsevier
DO  - 10.1016/j.crma.2009.07.011
LA  - en
ID  - CRMATH_2009__347_17-18_1007_0
ER  -

%0 Journal Article
%A M. Zuhair Nashed
%A Qiyu Sun
%A Wai-Shing Tang
%T Average sampling in $ {L}^{2}$
%J Comptes Rendus. Mathématique
%D 2009
%P 1007-1010
%V 347
%N 17-18
%I Elsevier
%R 10.1016/j.crma.2009.07.011
%G en
%F CRMATH_2009__347_17-18_1007_0

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

References
Cited by

[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

Cited by Sources:

Comments - Policy