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

Published online by Cambridge University Press:  19 December 2016

G. A. M. VELASCO  and
M. DÖRFLER
G. A. M. VELASCO
Affiliation:
Institute of Mathematics, University of the Philippines Diliman, 1101 Quezon City, Philippines email: gamvelasco@math.upd.edu.ph
M. DÖRFLER
Affiliation:
Numerical Harmonic Analysis Group, Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria email: monika.doerfler@univie.ac.at
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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.

Keywords

framesmultiplierssampling theorysignal theory (filtering, reconstruction)approximation by other special function classes
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 5 , October 2017 , pp. 854 - 876
Copyright
Copyright © Cambridge University Press 2016 

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