Haar wavelet
= Haar wavelet
{c}
{title2=$\psi=\chi_{[0,1/2)}-\chi_{[1/2,1)}$}
{wiki}
The Haar wavelet has one <vanishing moment> and <compact support> of unit length. Its <scaling function> is $\chi_{[0,1)}$, and its refinement coefficients are $h_0=h_1=1/\sqrt2$. The approximation spaces consist of functions constant on dyadic cells. Its discontinuity makes it effective for jump localization but limits smooth-function approximation.