Sampling theorems for nonstationary random processes

Lee, Alan J.

doi:10.1090/S0002-9947-1978-0482995-6

Sampling theorems for nonstationary random processes
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by Alan J. Lee PDF

Trans. Amer. Math. Soc. 242 (1978), 225-241 Request permission

Abstract:

Consider a second order stochastic process $\{ X(t),t \in \textbf {R}\}$, and let $H(X)$ be the Hilbert space generated by the random variables of the process. The process is said to be linearly determined by its samples $\{ X(nh),n \in \textbf {Z}\}$ if the random variables $X(nh)$ generate $H(X)$. In this paper we give a sufficient condition for a wide class of nonstationary processes to be determined by their samples, and present sampling theorems for such processes. We also consider similar problems for harmonizable processes indexed by LCA groups having suitable subgroups.

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