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