# Only random signal has PSD?

I heard from someone online who said: "Only random signal has PSD, determinate signal does not have. For example, period signal does not have PSD."

I am very astonishing about this statement, but it seems he is quite sure about his idea. In my opinion, both random signal and determinate signal have PSD, and it is the Fourier transform of the autocovariance of the signal. However, only stationary random and period signal have stable PSD. Am I right?

• You're on the right track. Note that the PSD is defined for all wide-sense stationary processes, which is a looser restriction than saying fully stationary processes. – Jason R Feb 27 '14 at 3:36

$$C_{XX}(t,s) = E\left[(X_t - \mu_t)(X_s - \mu_s)\right] = E[X_t X_s] - \mu_t \mu_s$$