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Math Help - fourier transform

  1. #1
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    fourier transform

    Show that following function is a covariance function by taking the fourier transform.

    C( τ) = σ˛exp {-a |τ |}(1+a|τ |+((aτ)˛)/3),a>=0

    I have done the fourier transform before but not sure how to integrate with the absolute value.So an explained solution would be very helpful.
    Last edited by johnnys; April 1st 2012 at 03:05 AM.
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  2. #2
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    Re: fourier transform

    I think you want to use Bochner's theorem, in the context of Probability theory: If the Fourier transform of the function C is a positive-definite complex-valued function, then C is a covariance function.
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