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On the Slepian process of a random Gaussian trigonometric polynomial

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2 Author(s)
Hasofer, A.M. ; Sch. of Math., New South Wales Univ., Kensington, NSW, Australia ; Ghahreman, S.

It is proved that the Slepian process of a stationary trigonometric polynomial with Gaussian coefficients has a Karhunen-Loeve expansion consisting of a finite number of terms, and that each eigenfunction is itself a finite trigonometric polynomial. Upper bounds for the error which results when replacing the Slepian process corresponding to a general Gaussian stationary process by the Slepian process corresponding to its finite trigonometric approximation are obtained. A numerical example is given and the results are used to estimate by simulation the distribution of the excursion time above a level of a particular Gaussian stationary process

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Information Theory, IEEE Transactions on  (Volume:35 ,  Issue: 4 )