A q-analogue of the Whittaker-Shannon-Kotelnikov sampling theorem
Abbreviated Journal Title
Proc. Amer. Math. Soc.
Shannon sampling theorem; band-limited and sinc functions; q-trigonometric series; basic hypergeometric functions; FOURIER; Mathematics, Applied; Mathematics
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-analogue of the Whittaker-Shannon-Kotel'nikov sampling theorem. The proof uses recent results in the theory of q-orthogonal polynomials and basic hypergeometric functions, in particular, new results on the addition theorems for q-exponential functions.
Proceedings of the American Mathematical Society
"A q-analogue of the Whittaker-Shannon-Kotelnikov sampling theorem" (2003). Faculty Bibliography 2000s. 3828.