# Gibbs Phenomenon

Introduced in MATH213 when learning about Fourier Series.

Gibbs Phenomenon

For a $L_{2}([a,b])$ function $f$ with periodic extension $f_{p}$, if $f_{p}$ is not continuous at some point $t_{0}$ then

truncatedFourier series of $f$ will have growing oscillations near the point $t_{0}$. This is called Gibbs Phenomenon.These oscillations do not appear in the infinite sum.