Year: 2025
Type: preprint
Abstract: In this article, we consider a variation of the existence of Gabor frames in a probabilistic setting, in which we consider time-frequency shifts taken over random-periodic sets. We demonstrate that the method of selecting random-periodic time-frequency shifts is successful with high probability for specific categories of well-behaved functions, notably including Hermite functions, totally positive functions, and B-spline functions. In particular, we show that if $x_1, x_2, \ldots ,x_m$ are independent and uniformly distributed in $[0,1),$ with $m$ sufficiently large, then the set of time-frequency shifts $Λ\times \ZZ, $ where $Λ=\ZZ + \{x_1, x_2, \ldots, x_m\},$ forms Gabor frame with high probability.
Source: arXiv (Cornell University)
Authors: Raj, Sarthak, Sivananthan, S.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409051419