On Sampling Stationary Stochastic Processes

Abstract

A quasi Fourier-type duality associated with a bandlimited stationary stochastic process can be established. It comes from the spectral representation of the process and a compact support assumption for its spectral density. In this way, for essentially bounded spectral densities we have an isometry between a weightedL²space and the Hilbert space spanned by the process. We can transfer converging expansions for the exponential complex e^itw in the :L²-space into a sampling expansion for the process converging in the mean square sense.

Keywords:

• Stationary stochastic processes
• sampling formulas
• Riesz bases
• reproducing kernel,
• Hilben spaces