A sampling theorem for stationary (wide sense) stochastic processes.

Abstract

where g is of bounded variation on [-h-/2, h-1/2] and the jumps of g at the endpoints, if any, are equal [3]. This result, or some variant of it, is known in the communications art as the sampling theorem [12]; it is widely usod in information theory [4]. In the present paper we seek conditions under which the random variables x(t) of a stationary (wide sense) stochastic process Ix(t), -oo 0 is to be regarded throughout as a nfxed preassigned number.) The problem is a simple one, intuitively speaking. Suppose process x contains a component aie2lriXlt at frequency Xi; this component contributes to the samples the quantities