Fourier coefficient decay
= Fourier coefficient decay
{c}
{title2=$|a_n|+|b_n|=O(n^{-p})$}
= Coefficient decay
{synonym}
The rate at which <Fourier coefficients> approach zero as their index increases. The differentiability of the <periodic extension>, including matching values and derivatives at its joins, controls this rate through <integration by parts>. An absolutely bounded tail $O(n^{-p})$ with $p>1$ gives a uniform truncation error $O(N^{1-p})$.