Confused about autocorrelation and PSD

  • Thread starter xaratustra
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I am confused a bit :confused:. I read in a paper that the following property holds, but can't find where it comes from.

[itex]\mathsf{E}\left[X(\omega)X^*(\omega')\right]=2\pi\delta(\omega-\omega')S_{XX}(\omega)[/itex]

it says that the expected value of the Fourier transformed signal is proportional to the spectral density function (PSD) [itex]S_{XX}(\omega)[/itex] which is as usual defined as:

[itex]S_{XX}(\omega)=\int_{-\infty}^{\infty}r_{XX}(\tau)e^{-i\omega\tau}\,d\tau[/itex]

Any one knows where this comes from?

thanks.
 

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