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Confused about autocorrelation and PSD

  1. Apr 18, 2012 #1
    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.
     
  2. jcsd
  3. Apr 18, 2012 #2

    Andy Resnick

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