Uncertainty principles for the short-time Fourier transform on the lattice
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909308095037440 |
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| author | Poria, Anirudha Dasgupta, Aparajita |
| author_facet | Poria, Anirudha Dasgupta, Aparajita |
| contents | In this paper, we study a few versions of the uncertainty principle for the short-time Fourier transform on the lattice $\mathbb Z^n \times \mathbb T^n$. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho--Stark's uncertainty principle, Benedicks-type uncertainty principle, Heisenberg-type uncertainty principle and local uncertainty inequality for this transform on $\mathbb Z^n \times \mathbb T^n$. Also, we obtain the Heisenberg-type uncertainty inequality using the $k$-entropy of the short-time Fourier transform on $\mathbb Z^n \times \mathbb T^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05886 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Uncertainty principles for the short-time Fourier transform on the lattice Poria, Anirudha Dasgupta, Aparajita Functional Analysis Primary 44A15, Secondary 42C20, 33C45 In this paper, we study a few versions of the uncertainty principle for the short-time Fourier transform on the lattice $\mathbb Z^n \times \mathbb T^n$. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho--Stark's uncertainty principle, Benedicks-type uncertainty principle, Heisenberg-type uncertainty principle and local uncertainty inequality for this transform on $\mathbb Z^n \times \mathbb T^n$. Also, we obtain the Heisenberg-type uncertainty inequality using the $k$-entropy of the short-time Fourier transform on $\mathbb Z^n \times \mathbb T^n$. |
| title | Uncertainty principles for the short-time Fourier transform on the lattice |
| topic | Functional Analysis Primary 44A15, Secondary 42C20, 33C45 |
| url | https://arxiv.org/abs/2204.05886 |