(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f be a suitably regular function on ℝ. (whatever that means).

What function do we obtain when we take the Fourier transform of the Fourier transform of f?

2. Relevant equations

[tex]F(s) = \int_{x=-\infty}^{\infty}f(x)e^{-2\pi isx}dx[/tex]

3. The attempt at a solution

[tex]\int_{x=-\infty}^{\infty}F(s)e^{-2\pi isx}dx = F(s)\int_{x=-\infty}^{\infty}e^{-2\pi isx}dx = F(s)[\frac{-e^{-2\pi isx}}{2\pi is}]_{x=-\infty}^{\infty} = \frac{F(s)i}{2\pi s}[e^{-2\pi isx}]_{x=-\infty}^{\infty}[/tex]

But this simply oscillates indefinitely around a complex circle as x goes to negative infinity and infinity, where have I gone wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: The Fourier transform of the Fourier transform

**Physics Forums | Science Articles, Homework Help, Discussion**