Spherical top-hat window function
= Spherical top-hat window function
{title2=$W_R$}
A spherical top-hat window function averages a field uniformly inside a <sphere> of radius $R$ and gives zero weight outside it. Its normalized real-space kernel is $W_R(\mathbf x)=3/(4\pi R^3)$ for $|\mathbf x|\leq R$, and its <Fourier transform> is
$$
\widetilde W_R(k)=3\frac{\sin(kR)-kR\cos(kR)}{(kR)^3}.
$$