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Sampling time-frequency localized functions and constructing localized time-frequency frames

  • G. A. M. VELASCO (a1) and M. DÖRFLER (a2)
Abstract

We study functions whose time-frequency content are concentrated in a compact region in phase space using time-frequency localization operators as a main tool. We obtain approximation inequalities for such functions using a finite linear combination of eigenfunctions of these operators, as well as a local Gabor system covering the region of interest. These would allow the construction of modified time-frequency dictionaries concentrated in the region.

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[2] A. Aldroubi , C. A. Cabrelli & U. Molter (2004) Wavelets on irregular grids with arbitrary dilation matrices, and frame atoms for L 2(ℝ d ). Appl. Comput. Harmon. Anal. (Special Issue: Frames in Harmonic Analysis, Part II) 17 (2), 119140.

[5] I. Daubechies (1988) Time-frequency localization operators: A geometric phase space approach. IEEE Trans. Inform. Theory 34 (4), 605612.

[8] M. Dörfler (2011) Quilted Gabor frames - A new concept for adaptive time-frequency representation. Adv. Appl. Math. 47 (4), 668687.

[9] M. Dörfler & E. Matusiak (2014) Nonstationary gabor frames - existence and construction. Int. J. Wavelets Multiresolut. Inf. Process. 12 (3).

[14] H. G. Feichtinger & N. Kaiblinger (2004) Varying the time-frequency lattice of Gabor frames. Trans. Amer. Math. Soc. 356 (5), 20012023.

[15] H. G. Feichtinger & K. Nowak (2001) A Szegö-type theorem for Gabor-Toeplitz localization operators. Michigan Math. J. 49 (1), 1321.

[17] H. G. Feichtinger & G. Zimmermann (1998) A Banach space of test functions for Gabor analysis. In: H. G. Feichtinger & T. Strohmer (editors), Gabor Analysis and Algorithms: Theory and Applications, Applied and Numerical Harmonic Analysis, Birkhäuser Boston, Boston, MA, pp. 123170.

[20] K. Gröchenig & J. Toft (2013) The range of localization operators and lifting theorems for modulation and Bargmann-Fock spaces. Trans. Amer. Math. Soc. 365, 44754496.

[23] H. J. Landau & H. O. Pollak (1961) Prolate spheroidal wave functions, Fourier analysis and uncertainty II. Bell Syst. Tech. J. 40, 6584.

[25] S. Li & H. Ogawa (2004) Pseudoframes for subspaces with applications. J. Fourier Anal. Appl. 10 (4), 409431.

[26] M. Liuni , A. Robel , E. Matusiak , M. Romito & X. Rodet (2013) Automatic adaptation of the time-frequency resolution for sound analysis and re-synthesis. IEEE Trans. Audio, Speech, Lang. Process. 21 (5), 959970.

[27] E. Matusiak & Y. C. Eldar (2012) Sub-Nyquist sampling of short pulses. IEEE Trans. Signal Process. 60 (3), 11341148.

[28] J. Ramanathan & P. Topiwala (1994) Time-frequency localization and the spectrogram. Appl. Comput. Harmon. Anal. 1 (2), 209215.

[30] D. Slepian & H. O. Pollak (1961) Prolate spheroidal wave functions, fourier analysis and uncertainty –I. Bell Syst. Tech. J. 40 (1), 4363.

[31] T. Strohmer (1998) Numerical algorithms for discrete Gabor expansions. In: H. G. Feichtinger and T. Strohmer (editors), Gabor Analysis and Algorithms: Theory and Applications, Birkhäuser Boston, Boston, 267294.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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