# Periodic kernel

The periodic kernel is an important prior when we're trying to model periodic functions with the gaussian process:

\begin{equation} K(x, x') = \sigma^{2} \, \exp\left(-\frac{2}{l^{2}} \sin^{2}\left(\pi \frac{|x-x'|}{p}\right)\right) \end{equation}
Where \(\sigma^2\) is the *amplitude*, \(l\) the *lengthscale* and \(p\) the *period*.