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Simulation of Stationary Process Via a Sampling Theorem

✍ Scribed by M. Grigoriu

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
394 KB
Volume
166
Category
Article
ISSN
0022-460X

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✦ Synopsis

A new simulation algorithm is developed for generating realizations of a stationary bandlimited Gaussian process. The algorithm is based on a parametric model that can be derived from a sampling theorem, and consists of a superposition of a finite set of deterministic functions of time with random amplitudes corresponding to values of the band-limited process at equally spaced time intervals. The parametric model is Gaussian, with mean and covariance functions that can be obtained from the second-moment characteristics of the band-limited process by elementary calculations. Moreover, the model approximates the band-limited process satisfactorily and is used to generate realizations of it. Simulation based on the model in the paper can be performed on-line, similar to techniques based on the ARMA model. Examples are presented to demonstrate the proposed algorithm and evaluate its performance.

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## Abstract Stochastic geometry models based on a stationary Poisson point process of compact subsets of the Euclidean space are examined. Random measures on ℝ^__d__^, derived from these processes using Hausdorff and projection measures are studied. The central limit theorem is formulated in a way