A weakly stationary, continuous-time stochastic process has spectral density [s(omega)= begin{cases}0 text { for }|omega| 2 omega_{0},

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A weakly stationary, continuous-time stochastic process has spectral density

\[s(\omega)= \begin{cases}0 \text { for }|\omega|<\omega_{0} & \text { or for }|\omega|>2 \omega_{0}, \\ a^{2} \text { for } & \omega_{0} \leq|\omega| \leq 2 \omega_{0},\end{cases}\]

Prove that its covariance function is given by

\[C(\tau)=2 a^{2} \sin \left(\omega_{0} \tau\right)\left(\frac{2 \cos \omega_{0} \tau-1}{\tau}\right)\]

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Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

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Question Posted: Apr 26, 2024 04:01 PM

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A weakly stationary, continuous-time stochastic process has spectral density [s(omega)= begin{cases}0 text { for }|omega| 2 omega_{0},

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Applied Probability And Stochastic Processes

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