# Fourier transform

```latex
\begin{aligned}
\widehat{f}(\xi)
  &= \int_{-\infty}^{\infty} f(x)e^{-2\pi i x\xi}\,dx,\\
f(x)
  &= \int_{-\infty}^{\infty}\widehat{f}(\xi)e^{2\pi i x\xi}\,d\xi.
\end{aligned}
```