
arXiv: 2204.05886
AbstractIn this paper, we study a few versions of the uncertainty principle for the short‐time Fourier transform on the lattice . 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 . Also, we obtain the Heisenberg‐type uncertainty inequality using the ‐entropy of the short‐time Fourier transform on .
Mathematics - Functional Analysis, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Donoho-Stark's uncertainty principle, short-time Fourier transform, FOS: Mathematics, Primary 44A15, Secondary 42C20, 33C45, Benedicks-type uncertainty principle, Heisenberg-type uncertainty inequality, Functional Analysis (math.FA)
Mathematics - Functional Analysis, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Donoho-Stark's uncertainty principle, short-time Fourier transform, FOS: Mathematics, Primary 44A15, Secondary 42C20, 33C45, Benedicks-type uncertainty principle, Heisenberg-type uncertainty inequality, Functional Analysis (math.FA)
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