# Why use cross-spectral density to calculate frequency response?

I am taking a class about system identification and currently learning about cross-spectral density. My textbook says that the frequency response, G, of a system can be determined as $$G=\frac{S_{uy}}{S_{uu}}$$ where $S_{uu}$ is the Fourier transform of the autocorrelation of the input, and $S_{uy}$ is the Fourier transform of the cross-correlation of the input and the output (the cross-spectral density).

Now, in basic control systems classes you lean that $G=\frac{Y}{U}$.

The former method, using the cross-spectral densities, seems to be related to this more basic calculation, but I'm unsure why we bother using the cross-spectral densities at all. Is it simply to help eliminate noise from the signals or is there some other reason for it?

Thanks!