Random Sampling of Mellin Band-Limited Signals

In this paper, we address the random sampling problem for the class of functions in the space of Mellin band-limited functions BT, which are concentrated on a bounded cube. It is established that any Mellin band-limited function can be approximated by an element in a finite-dimensional subspace of BT. Utilizing the notion of covering number and Bernstein's inequality to the sum of independent random variables, we prove that the probabilistic sampling inequality holds for the set of concentrated signals in BT with an overwhelming probability provided the sampling size is large enough.