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- Title
Uncertainty principles for the short‐time Fourier transform on the lattice.
- Authors
Poria, Anirudha; Dasgupta, Aparajita
- 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$\mathbb {Z}^n \times \mathbb {T}^n$.
- Subjects
FOURIER transforms; ENTROPY; LATTICE field theory; HEISENBERG uncertainty principle; QUANTUM entropy
- Publication
Mathematische Nachrichten, 2024, Vol 297, Issue 4, p1501
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.202200151