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

Anirudha Poria and Aparajita Dasgupta

Mathematische Nachrichten, 2024, vol. 297, issue 4, 1501-1518

Abstract: In this paper, we study a few versions of the uncertainty principle for the short‐time Fourier transform on the lattice Zn×Tn$\mathbb {Z}^n \times \mathbb {T}^n$. 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 Zn×Tn$\mathbb {Z}^n \times \mathbb {T}^n$. Also, we obtain the Heisenberg‐type uncertainty inequality using the k$k$‐entropy of the short‐time Fourier transform on Zn×Tn$\mathbb {Z}^n \times \mathbb {T}^n$.

Date: 2024
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https://doi.org/10.1002/mana.202200151

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