Title :
On the Slepian process of a random Gaussian trigonometric polynomial
Author :
Hasofer, Abraham M. ; Ghahreman, Shahaboddin
Author_Institution :
Sch. of Math., New South Wales Univ., Kensington, NSW, Australia
fDate :
7/1/1989 12:00:00 AM
Abstract :
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
Keywords :
information theory; polynomials; random processes; Karhunen-Loeve expansion; Slepian process; eigenfunction; excursion time; finite trigonometric approximation; random Gaussian trigonometric polynomial; stationary trigonometric polynomial; upper bounds; Australia; Eigenvalues and eigenfunctions; Fatigue; Gaussian processes; Helium; Mathematics; Polynomials; Random variables; Stochastic processes; Upper bound;
Journal_Title :
Information Theory, IEEE Transactions on
