Sampling expansions for discrete transforms and their relationship with interpolation series
Mahmoud Hamed Annaby · Analysis · 1998
Kramer's sampling theorem gives us the possibility to reconstruct integral transforms from their values at sequences of real numbers. It is known that this theorem includes the Whittaker-Shannon-Kotel'nikov (WSK) sampling theorem, and that many Kramer-type expansions can be written in forms of Lagrange-type interpolation series. Here we introduce a discrete version of Kramer's theorem and prove that the discrete theorem is equivalent to Kramer's theorem. The WSK sampling theorem is shown to be included in the new theorem. Moreover, the relationship between the sampling expansions of the discrete transforms and the interpolation expansions is discussed. (orig.)