Abstract:
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition, band-limited functions can have very slow decay which translates in poor reconstruction. In this article we study the sampling problem in general shift invariant spaces. We characterize the functions in these spaces and provide necessary and sufficient conditions for a function in L2(R) to belong to a sampling space. Furthermore, we obtain decompositions of a sampling space in sampling subspaces. These decompositions are related with determining sets. Some examples are provided. © 2003 Sampling Publishing.
Registro:
Documento: |
Artículo
|
Título: | Functions in sampling spaces |
Autor: | Blanco, C.; Cabrelli, C.; Heineken, S. |
Filiación: | Depto. de Matemática, Univ. de Buenos Aires, Pab. I, 1428 Capital Federal, Argentina Depto. de Matemática, Univ. de Buenos Aires, CONICET, Pab. I, 1428 Capital Federal, Argentina
|
Palabras clave: | Determining sets; Frames; Sampling spaces; Shift invariant spaces |
Año: | 2006
|
Volumen: | 5
|
Número: | 3
|
Página de inicio: | 275
|
Página de fin: | 295
|
Título revista: | Sampling Theory in Signal and Image Processing
|
Título revista abreviado: | Sampl.Theory Signal Image Proces.
|
ISSN: | 15306429
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v5_n3_p275_Blanco |
Referencias:
- Aldroubi, A., Cabrelli, C., Hardin, D., Molter, U., Rodado, A., Determining sets of shift invariant spaces (2003) Wavelets and Its Applications, pp. 1-8. , (Chennai, January 2002), M. Chrisna, R. Radha and S. Thangavelu, eds., Allied Publishers, New Delhi
- Aldroubi, A., Gröchenig, K., Nonuniform sampling and reconstruction in shift-invariant spaces (2001) SIAM Rev., 43 (4), pp. 585-620
- Bownik, M., The structure of shift-invariant subspaces of L2 (Rn) (2000) J. Funct. Anal., 177 (2), pp. 282-309
- de Boor, C., DeVore, R., Ron, A., Approximation from shift-invariant subspaces of L2 (Rd) (1994) Trans. Amer. Math. Soc., 341, pp. 787-806
- Benedetto, J.J., Ferreira, P., (2004) Modern Sampling Theory, , Birkhäuser, Boston
- Benedetto, J.J., Li, S., The theory of multi-resolution analysis frames and applications to filter banks (1998) Appl. Comp. Harm. Anal., 5, pp. 389-427
- Benedetto, J.J., Zayed, A., (2001) Sampling, Wavelets, and Tomography, , Birkhäuser, Boston
- Chen, W., Han, B., Jia, R.Q., On simple oversampled A/D conversion in shift invariant spaces (2005) IEEE Trans. Inform. Theory, 2 (51), pp. 648-657
- Chen, W., Itoh, S., Shiki, J., On sampling in shift invariant spaces (2002) IEEE Trans. Inform. Theory, 48 (10), pp. 2802-2810
- Chen, W., Itoh, S., A sampling theorem for shift invariant subspaces (1998) IEEE Trans. Signal Process., 46 (10), pp. 2822-2824
- Christensen, O., (2003) An Introduction to Frames and Riesz Basis, , Birkhäuser, Boston
- Gröchenig, K., (2001) Foundations of Time-Frecuency Analysis, , Birkhäuser, Boston
- Janssen, A., The Zak transform: A signal transform for sampled time-continuous signals (1988) Philips J. Res., 43 (1), pp. 23-69
- Sun, W., Sampling theorems for multivariate shift invariant subspaces (2005) Sampl. Theory Signal Image Process., 4 (1), pp. 73-98
- Sun, W., Zhou, X., On the sampling theorem for wavelet subspaces (1999) J. Fourier Anal. Appl., 5, pp. 347-354
- Sun, W., Zhou, X., (2004) An Aspect of the Sampling Theorem, Multiresolution and Information Processing, , International Journal of Wavelets, In Press
- Walter, G., A sampling theorem for wavelet subspaces (1992) IEEE Trans. Inform. Theory, 38 (2), pp. 881-884
Citas:
---------- APA ----------
Blanco, C., Cabrelli, C. & Heineken, S.
(2006)
. Functions in sampling spaces. Sampling Theory in Signal and Image Processing, 5(3), 275-295.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v5_n3_p275_Blanco [ ]
---------- CHICAGO ----------
Blanco, C., Cabrelli, C., Heineken, S.
"Functions in sampling spaces"
. Sampling Theory in Signal and Image Processing 5, no. 3
(2006) : 275-295.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v5_n3_p275_Blanco [ ]
---------- MLA ----------
Blanco, C., Cabrelli, C., Heineken, S.
"Functions in sampling spaces"
. Sampling Theory in Signal and Image Processing, vol. 5, no. 3, 2006, pp. 275-295.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v5_n3_p275_Blanco [ ]
---------- VANCOUVER ----------
Blanco, C., Cabrelli, C., Heineken, S. Functions in sampling spaces. Sampl.Theory Signal Image Proces. 2006;5(3):275-295.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15306429_v5_n3_p275_Blanco [ ]