A note on the sampling principle for continuous signals

Abstract

Two sampling (integral interpolation) theorems for continuous signals (continuous parameter stochastic processes) are proved. The first of these is the sampling principle introduced by Shannon, precise formulation or proof of which has not appeared hitherto. Obtained as a secondary result in this connection is a generalization of a result on the spectra of sampled signals given by Bennet. The second theorem is a stochastic version of the Newton-Gauss interpolation formula as representative of a different class of sampling theorems.