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signal theory (filtering, reconstruction)

European Journal of Applied Mathematics (1)

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Sampling time-frequency localized functions and constructing localized time-frequency frames
G. A. M. VELASCO, M. DÖRFLER
Journal:

European Journal of Applied Mathematics / Volume 28 / Issue 5 / October 2017

Published online by Cambridge University Press:

19 December 2016, pp. 854-876
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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.