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Fourier transform

  1. Apr 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Just something I am working through and am a bit stuck on.

    2. Relevant equations

    I have taken the fourier transform of an RC circuit which gives me :
    Y(ω)=((X(ω))/(1+iωτ))
    If i take the voltage across the circuit as white noise then i get:
    Y(ω)=σ^²/2π/(1+iωτ))
    How can i find the variance function and covariance of this fourier transform
    3. The attempt at a solution
    I am not sure how to do this
     
  2. jcsd
  3. Apr 12, 2012 #2

    marcusl

    User Avatar
    Science Advisor
    Gold Member

    First, welcome to PF. Regarding your questions, why are you trying to find these? Y is a complex function, so what do you even mean by variance? Individual variances of real and imaginary parts? Of its power spectral density |Y|^2?

    The variances of Real(Y) and Imag(Y) are the third and second moments of a function known in statistics as a Cauchy distribution, and these moments are undefined. |Y|^2 is the Cauchy distribution itself, and it has undefined first and second moments (mean and variance).
     
    Last edited: Apr 12, 2012
  4. Apr 12, 2012 #3
    Of the spectral density which is X(ω)/(1+(ωτ)^2)) i had incorectly stated it in the post.
     
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