Question: A weakly stationary continuous-time process has covariance function [C(tau)=a^{-b tau^{2}} text { for } a>0, b>0] Prove that its spectral density is given by [s(omega)=frac{a}{2

A weakly stationary continuous-time process has covariance function

\[C(\tau)=a^{-b \tau^{2}} \text { for } a>0, b>0\]

Prove that its spectral density is given by

\[s(\omega)=\frac{a}{2 \sqrt{\pi b}} e^{-\frac{\omega^{2}}{4 b}}\]

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