Artículo

Cabrelli, C.; Lee, D.G.; Molter, U.; Pfander, G.E. "Time-frequency shift invariance of Gabor spaces generated by integer lattices" (2019) Journal of Mathematical Analysis and Applications. 474(2):1289-1305
El editor solo permite decargar el artículo en su versión post-print desde el repositorio. Por favor, si usted posee dicha versión, enviela a
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We study extra time-frequency shift invariance properties of Gabor spaces. For a Gabor space generated by an integer lattice, we state and prove several characterizations for its time-frequency shift invariance with respect to a finer integer lattice. The extreme cases of full translation invariance, full modulation invariance, and full time-frequency shift invariance are also considered. The results show a close analogy with the extra translation invariance of shift-invariant spaces. © 2019 Elsevier Inc.

Registro:

Documento: Artículo
Título:Time-frequency shift invariance of Gabor spaces generated by integer lattices
Autor:Cabrelli, C.; Lee, D.G.; Molter, U.; Pfander, G.E.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
IMAS/CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Lehrstuhl für Mathematik – Wissenschaftliches Rechnen, Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt-Ingolstadt, Eichstätt, 85071, Germany
Palabras clave:Extra time-frequency shift invariance; Gabor space; Shift-invariant space; Time-frequency analysis
Año:2019
Volumen:474
Número:2
Página de inicio:1289
Página de fin:1305
DOI: http://dx.doi.org/10.1016/j.jmaa.2019.02.017
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v474_n2_p1289_Cabrelli

Referencias:

  • Aldroubi, A., Cabrelli, C., Heil, C., Kornelson, K., Molter, U., Invariance of a shift-invariant space (2010) J. Fourier Anal. Appl., 16, pp. 60-75
  • Aldroubi, A., Sun, Q., Wang, H., Uncertainty principles and Balian–Low type theorems in principal shift-invariant spaces (2011) Appl. Comput. Harmon. Anal., 30, pp. 337-347
  • Anastasio, M., Cabrelli, C., Paternostro, V., Extra invariance of shift-invariant spaces on LCA groups (2010) J. Math. Anal. Appl., 370, pp. 530-537
  • Anastasio, M., Cabrelli, C., Paternostro, V., Invariance of a shift-invariant space in several variables (2011) Complex Anal. Oper. Theory, 5, pp. 1031-1050
  • Bölcskei, H., Orthogonal frequency division multiplexing based on offset QAM (2003) Advances in Gabor Analysis, pp. 321-352. , H.G. Feichtinger T. Strohmer Birkhäuser Boston
  • Bownik, M., The structure of shift-modulation invariant spaces: the rational case (2007) J. Funct. Anal., 244, pp. 172-219
  • Cabrelli, C., Molter, U., Pfander, G.E., Time-frequency shift invariance and the Amalgam Balian–Low theorem (2016) Appl. Comput. Harmon. Anal., 41, pp. 677-691
  • Cabrelli, C., Lee, D.G., Molter, U., Pfander, G.E., Extra invariance and Balian–Low type obstructions for Gabor spaces (2017) 2017 International Conference on Sampling Theory and Applications, (SampTA), Tallin, pp. 391-395
  • Caragea, A., Lee, D.G., Pfander, G.E., Philipp, F., A Balian–Low theorem for subspaces (2018) J. Fourier Anal. Appl., , in press
  • de Boor, C., DeVore, R., Ron, A., Approximation from shift-invariant subspaces of L 2 (R d ) (1994) Trans. Amer. Math. Soc., 341, pp. 787-806
  • de Boor, C., DeVore, R., Ron, A., The structure of finitely generated shift-invariant spaces in L 2 (R d ) (1994) J. Funct. Anal., 119, pp. 37-78
  • Feichtinger, H.G., Zimmermann, G., A Banach space of test functions for Gabor analysis (1998) Gabor Analysis and Algorithms: Theory and Applications, pp. 123-170. , H.G. Feichtinger T. Strohmer Birkhäuser Boston
  • Gröchenig, K., Foundations of Time-Frequency Analysis (2001) Appl. Numer. Harmon. Anal., , Birkhäuser
  • Hardin, D.P., Northington, M.C., V, Powell, A.M., A sharp Balian–Low uncertainty principle for shift-invariant spaces (2016) Appl. Comput. Harmon. Anal., 44, pp. 294-311
  • Heil, C., History and evolution of the density theorem for Gabor frames (2007) J. Fourier Anal. Appl., 13, pp. 113-166
  • Heil, C., Walnut, D., Continuous and discrete wavelet transforms (1989) SIAM Rev., 31, pp. 628-666
  • Hewitt, E., Ross, K.A., Abstract Harmonic Analysis, vol. I: Structure of Topological Groups, Integration Theory, Group Representations (1963) Grundlehren Math. Wiss., 115. , Springer-Verlag Berlin
  • Kozek, W., Molisch, A.F., Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels (1998) IEEE J. Sel. Areas Commun., 16, pp. 1579-1589

Citas:

---------- APA ----------
Cabrelli, C., Lee, D.G., Molter, U. & Pfander, G.E. (2019) . Time-frequency shift invariance of Gabor spaces generated by integer lattices. Journal of Mathematical Analysis and Applications, 474(2), 1289-1305.
http://dx.doi.org/10.1016/j.jmaa.2019.02.017
---------- CHICAGO ----------
Cabrelli, C., Lee, D.G., Molter, U., Pfander, G.E. "Time-frequency shift invariance of Gabor spaces generated by integer lattices" . Journal of Mathematical Analysis and Applications 474, no. 2 (2019) : 1289-1305.
http://dx.doi.org/10.1016/j.jmaa.2019.02.017
---------- MLA ----------
Cabrelli, C., Lee, D.G., Molter, U., Pfander, G.E. "Time-frequency shift invariance of Gabor spaces generated by integer lattices" . Journal of Mathematical Analysis and Applications, vol. 474, no. 2, 2019, pp. 1289-1305.
http://dx.doi.org/10.1016/j.jmaa.2019.02.017
---------- VANCOUVER ----------
Cabrelli, C., Lee, D.G., Molter, U., Pfander, G.E. Time-frequency shift invariance of Gabor spaces generated by integer lattices. J. Math. Anal. Appl. 2019;474(2):1289-1305.
http://dx.doi.org/10.1016/j.jmaa.2019.02.017