Abstract:
In this paper we study the question of the representation of random variables by means of frames or Riesz basis generated by stationary sequences. This concerns to the possible representation of continuous time processes by means of discrete samples. © 2010 IEEE.
Registro:
| Documento: |
Conferencia
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| Título: | Stationary sequences and stable sampling |
| Autor: | Medina, J.M.; Frías, B.C. |
| Ciudad: | Taichung |
| Filiación: | Departamento de Matemática, Universidad de Buenos Aires, CONICET, Paseo Colón 850, Buenos Aires, Argentina
Departamento de Electrónica, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, Buenos Aires, Argentina
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| Palabras clave: | Continuous time; Discrete sample; Riesz basis; Random variables; Spectroscopy; Information theory |
| Año: | 2010
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| Página de inicio: | 94
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| Página de fin: | 99
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| DOI: |
http://dx.doi.org/10.1109/ISITA.2010.5649510 |
| Título revista: | 2010 20th International Symposium on Information Theory and Its Applications, ISITA 2010 and the 2010 20th International Symposium on Spread Spectrum Techniques and Applications, ISSSTA 2010
|
| Título revista abreviado: | ISITA/ISSSTA - Int. Symp. Inf. Theory Its Appl.
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97814244_v_n_p94_Medina |
Referencias:
- Beaty, M.G., Dodson, M.M., The WKS Theorem, Spectral Translates and Plancherel's Formula (2004) J. Fourier Anal. Appl., 10 (2), pp. 179-199
- Benedetto, J.J., Li, S., The theory of multiresolution analysis frames and applications to filter banks (1998) Appl. Comput. Harmon. Anal., 5, pp. 389-427
- Bownik, M., The structure of shift invariant subspaces of L2(ℝ) (2000) J. Funct. Anal., 177 (2), pp. 282-309
- De Boor, C., DeVore, R., Ron, A., The structure of finitely generated shiftinvariant spaces in L 2(ℝd) (1994) J. Funct. Anal., 119 (1), pp. 37-78
- Christensen, O., (2008) Frames and Bases. Applied and Numerical Harmonic Analysis Series, , Birkhäuser
- Dym, H., McKean, H.P., (1976) Gaussian Processes, Function Theory and the Inverse Spectral Problem, , Academic Press
- Gröchenig, K., (2001) Time Frequency Analysis, , Birkhäuser
- Houdré, C., On the Almost Sure convergence of series of stationary and related non stationary random variables (1995) Ann. Prob., 23 (3), pp. 1204-1218
- Ibragimov, I.A., Rozanov, Y.A., (1978) Gaussian Random Processes, , Springer Verlag
- Kwapien, S., Woyczynski, W.A., (1992) Random Series and Stochastic Integrals Single and Multiple, , Birkhäuser
- Lee, A.J., Sampling theorems for non stationary random processes (1978) Trans. Amer. Math. Soc., 242, pp. 225-241
- Lloyd, S.P., A sampling theorem for stationary (wide sense) stochastic processes (1959) Trans. Amer. Math. Soc., 92 (1), pp. 1-12
- Loéve, M., (1977) Probability Theory, 2. , Springer Verlag
- Lu, Y.M., Do, M.N., A Theory for sampling signals from a union of subspaces (2008) IEEE Trans. Signal Proc., 56 (6), pp. 2334-2345
- Masani, P., Shift invariant spaces and prediction theory (1962) Acta Math., 107, pp. 275-290
- Ron, A., Shen, Z., Frames and stable bases for shift -invariant subspaces of L 2(ℝd) (1995) Canad. J. Math., 47, pp. 1051-1094
- Rosenblatt, M., (1985) Stationary Sequences and Random Fields, , Birkhäuser
- Rozanov, Y.A., (1967) Stationary Random Processes, , Holden-Day
- Rozanov, Y.A., On stationary sequences forming a basis (1960) Soviet Math.-Doklady, 1, pp. 91-93
- Weron, A., On characterizations of interpolable and minimal stationary processes (1974) Studia Math., 49, pp. 165-183
- Makagon, A., Weron, A., Q-variate minimal stationary processes (1976) Studia Math., 59, pp. 41-52
- Wiener, N., Masani, P., The prediction theory of multivariate stochastic processes,II. The linear predictor (1959) Acta Math., 99, pp. 94-137
- Wojtaszczyc, P., (1991) Banach Spaces for Analysts, , Cambridge
- Zhao, P., Lin, G., Zhao, C., A matrix-valued wavelet KL-like expansion for wide sense stationary processes (2004) IEEE Trans. Signal Proc., 52 (4), pp. 914-920A4 - Society of Information Theory and Its Applications (SITA); National Science Council; Bureau of Foreign Trade, MOEA; Chunghwa Telecom Co., Ltd; Inf. Commun. Res. Lab. Ind. Technol.
Citas:
---------- APA ----------
Medina, J.M. & Frías, B.C.
(2010)
. Stationary sequences and stable sampling. 2010 20th International Symposium on Information Theory and Its Applications, ISITA 2010 and the 2010 20th International Symposium on Spread Spectrum Techniques and Applications, ISSSTA 2010, 94-99.
http://dx.doi.org/10.1109/ISITA.2010.5649510---------- CHICAGO ----------
Medina, J.M., Frías, B.C.
"Stationary sequences and stable sampling"
. 2010 20th International Symposium on Information Theory and Its Applications, ISITA 2010 and the 2010 20th International Symposium on Spread Spectrum Techniques and Applications, ISSSTA 2010
(2010) : 94-99.
http://dx.doi.org/10.1109/ISITA.2010.5649510---------- MLA ----------
Medina, J.M., Frías, B.C.
"Stationary sequences and stable sampling"
. 2010 20th International Symposium on Information Theory and Its Applications, ISITA 2010 and the 2010 20th International Symposium on Spread Spectrum Techniques and Applications, ISSSTA 2010, 2010, pp. 94-99.
http://dx.doi.org/10.1109/ISITA.2010.5649510---------- VANCOUVER ----------
Medina, J.M., Frías, B.C. Stationary sequences and stable sampling. ISITA/ISSSTA - Int. Symp. Inf. Theory Its Appl. 2010:94-99.
http://dx.doi.org/10.1109/ISITA.2010.5649510