# Thread: Fouriertransform attitude

1. ## 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

2. Originally Posted by Rapha
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