Let $X_t$ be a real w.s.s. random process. Its spectrum is given by $S(f)=\mathcal{F}R_X(\tau)(f)$ where $R_X$ is the process autocorrelation. As $X_t$ is real, the spectrum will be real and symmetric.
In deterministic signals, we can perform the Fourier transform on the signal and obtain two functions: the amplitude and the phase. The amplitude shows the presence of various frequencies in the signal, whereas the phase indicates the 'locations', noncontinuities, etc.
However, in random processes, as we perform Fourier transform on the autocorrelation, we get only the sense of the Fourier amplitude. Is there a measurement that can be performed in order to get some sort of "Fourier phase" for a random process?
Thanks.