  In this paper we review the Heisenberg uncertainty principle in a discrete
setting and, as in the classical uncertainty principle, we give it a dynamical
sense related to the discrete Schr\"odinger equation. We study the convergence
of the relation to the classical uncertainty principle, and, as a counterpart,
we also obtain another discrete uncertainty relation that does not have an
analogous form in the continuous case. Moreover, in the case of the Discrete
Fourier Transform, we give a inequality that allows us to relate the minimizer
to the Gaussian.
