Definition issue frequency domain - Random Signal Processing

[Tamis]

Hello i have a question about Random Signal Processing and the frequency domain. If i understand correctly one cannot use the Fourier transform to represent a stochastic process in the frequency domain. What is therefore used is the Power Spectral Density:

$S_X(f)=F\{R_X(\tau)\}$​

Were $F$ denotes the Fourier transform and $R_X(\tau)$ the auto correlation of the stochastic process $X$.

Now in the text i read definitions like $H(f)=\frac{Y(f)}{W(f)}$ were $W(f)$ is the input stochastic process. And I'm confused, is $W(f)$ the same as $S_W(f)$ or are they different?

 

[Valkarie]

Yes, W(f) is the same as S_W(f). The Power Spectral Density (PSD) is a measure of the power of a signal as a function of frequency. The PSD is related to the Fourier transform of a signal, but it is actually calculated from the auto-correlation of the signal. The PSD can be used to determine the frequency content of a signal and how it changes over time. In the equation H(f)=\frac{Y(f)}{W(f)}, W(f) is the PSD of the input stochastic process.