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

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

arXiv admin note: substantial text overlap with arXiv:2107.00954

References in corpus (1)

• Localization Operators On Discrete Modulation Spaces