I am reading in a book called "Understanding Jitter and Phase Noise" and came across the following equation and need a little help to understand his justification for a certain step in the derivation of the Power Spectral Density (PSD).
Assume we have a random process ${\phi(t)}$ which represents the random excess phase in $$v(t)=A Sin(w_{0}t+\phi(t))$$ Assume the amplitude is constant and we will perform the small angle approximation, such as excess phase ${\phi(t)}$ is less than one, which gives: $$v(t)=A Sin(w_{0}t)+A\phi(t)Cos(w_{0}t)$$ Assume the autocorrelation function of ${\phi(t)}$ is given by ${R_{\phi}(\tau)}$, so the autocorrelation of ${v(t)}$ is the following: $$R_{v}(t,\tau)=\frac{A^{2}}{2}[Cos(w_{0}\tau)-Cos(2w_{0}t+w_{0}\tau)+[Cos(2w_{0}t+w_{0}\tau)+Cos(w_{0}\tau)]R_{\phi}(\tau)]$$ It is noticed that ${R_{v}(t,\tau)}={R_{v}(t+T,\tau)}$, so it is cyclostationary process, what I do not understand is next. It is written we will take the average value over one period
$$R_{v,avg}(\tau)=\frac{1}{T}\int_{0}^{T}R_{v}(t,\tau)=\frac{A^{2}}{2}Cos(w_{0}\tau)[1+R_{\phi}(\tau)]$$ We can now find the PSD easily, what is the justification for the averaging that was made? I guess that is made to make the autocorrelation function only in the time difference {$\tau$} not in the absolute time, I guess if it is function in absolute time then there is no PSD defined in that case? I know this is possible if the cyclostationary process is further randomized by a random phase shift in the time, but this is not explicitly written here.