# Power Spectral Densities and transfer functions

## Main Question or Discussion Point

Hi

I know the PSD S of a free-running oscillator, describing its frequency fluctuations. Now, say that I want to consider the effect a standard PID circuit (with transfer function H) has on the oscillator.

I read in a paper that the resulting PSD of the locked oscillator becomes the product between H^2 and S. Is this really the case? It doesn't seem very logical to me that we are allowed to simply multiply these.

I'd be happy if someone can confirm this and possibly (shortly!) explain why. As an alternative, I'd be happy to get a reference to an article/book that describes it.

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