A 𝑞-analogue of the Whittaker-Shannon-Kotel’nikov sampling theorem

Abstract

The Whittaker-Shannon-Kotel’nikov (WSK) sampling theorem plays an important role not only in harmonic analysis and approximation theory, but also in communication engineering since it enables engineers to reconstruct analog signals from their samples at a discrete set of data points. The main aim of this paper is to derive a q q -analogue of the Whittaker-Shannon-Kotel’nikov sampling theorem. The proof uses recent results in the theory of q q -orthogonal polynomials and basic hypergeometric functions, in particular, new results on the addition theorems for q q -exponential functions.