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
\[ f(x) = \int_{-\infty}^{+\infty} e^{2\pi\,i\,x\,k} F(k) \, \mathrm{d}k \]