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Math Help - Fouriertransform attitude

  1. #1
    Senior Member
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    Nov 2008
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    Fouriertransform attitude

    Hi.

    I need to show that

    \int_{\mathbb{R}} |f(x)|^2 dx = \int_{\mathbb{R}} |\hat{f}(k)|^2 dk

    \hat{f} denotes the fourier transform

    \hat{f}(k) = \frac{1}{2\pi} \int_{\mathbb{R}} e^{ikx}f(x) dx

    I have no clue on this.

    Any comments are appreciated.

    Rapha
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Rapha View Post
    Hi.

    I need to show that

    \int_{\mathbb{R}} |f(x)|^2 dx = \int_{\mathbb{R}} |\hat{f}(k)|^2 dk

    \hat{f} denotes the fourier transform

    \hat{f}(k) = \frac{1}{2\pi} \int_{\mathbb{R}} e^{ikx}f(x) dx

    I have no clue on this.

    Any comments are appreciated.

    Rapha
    A rough proof of Parseval's theorem may be found here (rough in the sense of not saying why we can change the order of integration).

    CB
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