I have a signal ($S(t)$) which is product of a Gaussian ($G(t)$) and a random phase function ($e^{i\theta(t)}$, here $\theta(t)$ is a random function), as shown below
$S(t)=G(t).e^{i\theta(t)}$
If I calculate the auto correlation of such a signal ($E[S^*(t)S(t−τ)]$) it turns out to be a complex quantity and the same goes with the spectral density (Fourier transform of the auto-correlation function). My questions are the following.
- If the above analysis valid? as the process is not wide sense stationary.
- If the analysis is not valid, is there some way to handle this kind of situation?
- If the analysis is valid, What does the complex spectral density signifies?