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

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