Vanishing moment
= Vanishing moment
{title2=$\int x^r\psi(x)\,dx=0$}
A <wavelet> has $q$ vanishing moments when these integrals vanish for $0\le r<q$. For <compact support>, this is equivalent to a zero of order at least $q$ at the origin of its <Fourier transform>. Such a <wavelet> annihilates <polynomials> of degree less than $q$, and a <Taylor polynomial> bounds coefficients on smooth regions.