Discrete Sampling Theorem, Sinc-lets and Other Peculiar Properties of Sampled Signals

Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from their sparse samples are discussed for different transforms and applications are illustrated by examples of image super-resolution from multiple chaotically sampled frames and in image reconstruction from projections. Experimental evidence is presented of the existence of discrete signals sharply bounded both in space and DFT or DCT domains and of the family of the corresponding basis functions