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arXiv · 2204.05886

Uncertainty principles for the short-time Fourier transform on the lattice

Anirudha Poria·Aparajita Dasgupta
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Abstract

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 $\mathbb Z^n \times \mathbb T^n$.

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BibTeXRIS

Anirudha Poria, Aparajita Dasgupta. 2022-04-12. Uncertainty principles for the short-time Fourier transform on the lattice. https://doi.org/10.1002/mana.202200151

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