Gabor frames generated by Random-Periodic time-frequency shifts
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917968418439168 |
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| author | Raj, Sarthak Sivananthan, S. |
| author_facet | Raj, Sarthak Sivananthan, S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20259 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gabor frames generated by Random-Periodic time-frequency shifts Raj, Sarthak Sivananthan, S. Functional Analysis 42C15, 42A61 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. |
| title | Gabor frames generated by Random-Periodic time-frequency shifts |
| topic | Functional Analysis 42C15, 42A61 |
| url | https://arxiv.org/abs/2503.20259 |