From completeness of discrete translates to phaseless sampling of the short-time Fourier transform
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913812526923776 |
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| author | Grohs, Philipp Liehr, Lukas Shafkulovska, Irina |
| author_facet | Grohs, Philipp Liehr, Lukas Shafkulovska, Irina |
| contents | We study the uniqueness problem in short-time Fourier transform phase retrieval by exploring a connection to the completeness problem of discrete translates. Specifically, we prove that functions in $L^2(K)$ with $K \subseteq \mathbb{R}^d$ compact, are uniquely determined by phaseless lattice-samples of its short-time Fourier transform with window function $g$, provided that specific density properties of translates of $g$ are met. By proving completeness statements for systems of discrete translates in Banach function spaces on compact sets, we obtain new uniqueness statements for phaseless sampling on lattices beyond the known Gaussian window regime. Our results apply to a large class of window functions, which are relevant in time-frequency analysis and applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_05687 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | From completeness of discrete translates to phaseless sampling of the short-time Fourier transform Grohs, Philipp Liehr, Lukas Shafkulovska, Irina Functional Analysis Classical Analysis and ODEs Complex Variables 41A30, 42C30, 94A12, 94A20 We study the uniqueness problem in short-time Fourier transform phase retrieval by exploring a connection to the completeness problem of discrete translates. Specifically, we prove that functions in $L^2(K)$ with $K \subseteq \mathbb{R}^d$ compact, are uniquely determined by phaseless lattice-samples of its short-time Fourier transform with window function $g$, provided that specific density properties of translates of $g$ are met. By proving completeness statements for systems of discrete translates in Banach function spaces on compact sets, we obtain new uniqueness statements for phaseless sampling on lattices beyond the known Gaussian window regime. Our results apply to a large class of window functions, which are relevant in time-frequency analysis and applications. |
| title | From completeness of discrete translates to phaseless sampling of the short-time Fourier transform |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables 41A30, 42C30, 94A12, 94A20 |
| url | https://arxiv.org/abs/2211.05687 |