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?

  • $\begingroup$ 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. $\endgroup$ – Jason R Feb 27 '14 at 3:36

Autocovariance is defined on random signals.

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

The expected value only makes sense for random processes. You could treat a deterministic process as a random process where everything except for the one signal you observed has probability zero.

  • $\begingroup$ Is it infer that deterministic process does not have PSD or should not calculate PSD for such signal? $\endgroup$ – Kattern Mar 2 '14 at 11:56
  • $\begingroup$ @kattern: Perhaps the biggest concern is whether any PSD-like value is meaningful for your deterministic process. $\endgroup$ – MSalters Mar 10 '14 at 17:02
  • $\begingroup$ @MSalters I tread many vibration signals, which is not random in some extend. Do you think it is meaningless to use PSD in this case? What should I use in this case? $\endgroup$ – Kattern Mar 11 '14 at 17:14
  • $\begingroup$ I would assume your vibrations are random. The only way it would not be random is if the vibration happens the exact same way every time and that doesn't seem very likely. $\endgroup$ – Aaron Mar 11 '14 at 18:52
  • $\begingroup$ @Aaron There is a specific area to tread vibration with random excitation, which is known as Random Vibration. In other cases, we tread vibration as a deterministic process in some extend. Since this kind of vibration usually contains several eigen frequencies, we use PSD and other tools to reduce dimension of the data. What is you suggestion to trade this kind of signal? $\endgroup$ – Kattern Mar 12 '14 at 2:12

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