- #1
xaratustra
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I am confused a bit 
. 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.
. 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.