Uncertainty relation for multidimensional discrete signals

It is well-known that the famous uncertainty relation between duration and bandwidth of continuous-time signals can be appropriately modified to be applicable also to discrete-time signals, i.e. to signals which are mathematically represented by sequences of real or complex numbers. While the generalization of the uncertainty relation to signals defined on the multidimensional (continuous) real space is quite obvious, this task is less trivial in the case of discrete signals. It is the purpose of this paper to show that an uncertainty relation can also be formulated for multidimensional (MD) discrete signals. The MD signals reaching the uncertainty limit are composed of binomial coefficients and generalizations thereof.