The autocorrelation function of a Gaussian random process representing the unevenness of a road surface is given
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The autocorrelation function of a Gaussian random process representing the unevenness of a road surface is given by
\[R_{x}(\tau)=\sigma_{x}^{2} e^{-\alpha|v \tau|} \cos \beta v \tau\]
where \(\sigma_{x}^{2}\) is the variance of the random process and \(v\) is the velocity of the vehicle. The values of \(\sigma_{x}, \alpha\), and \(\beta\) for different types of road are as follows:
Compute the spectral density of the road surface for the different types of road.
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