# Fourier Transform

The Fourier transform of a function $$f$$ is given by the integral
\begin{align*} F(k) = \int_{-\infty}^{+\infty} e^{-2\pi\,i\,k\,x} f(x) \, \mathrm{d}x \end{align*}
where $$i$$ is the imaginary unit.
The inverse transform is given by
$f(x) = \int_{-\infty}^{+\infty} e^{2\pi\,i\,x\,k} F(k) \, \mathrm{d}k$

### Gallimaufry

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