I am confused a bit . I read in a paper that the following property holds, but can't find where it comes from.(adsbygoogle = window.adsbygoogle || []).push({});

[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 theFourier transformedsignal 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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# Confused about autocorrelation and PSD

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