Relevant sampling of the short-time Fourier transform of time-frequency localized functions

2017/07/30 by Gino Angelo Velasco, Velasco, Gino Angelo
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1707.09634

arxiv created 2017/07/30 · arxiv updated 2017/08/01

Abstract

We study the random sampling of the short-time Fourier transform of functions that are localized in a compact region in the time-frequency plane. We follow the approach introduced by Bass and Gröchenig for band-limited functions, and show that with a high, controllable probability, a sufficiently dense set of local random samples from the region of concentration in the time-frequency plane yields a sampling inequality for the short-time Fourier transform of time-frequency localized functions on the region.

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• Relevant sampling of band-limited functions
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• Sampling for approximating R-limited functions
• From completeness of discrete translates to phaseless sampling of the short-time Fourier transform