= Sharp-k smoothing filter
{title2=$\widetilde W(kR)=\mathbf1_{k<1/R}$}
= Sharp Fourier-space filter
{synonym}
A sharp-k filter includes every Fourier mode below a cutoff with unit weight and excludes all modes above it. For a <Gaussian random field>, increasing the cutoff adds independent Fourier shells, so the smoothed <density contrast> is a <Brownian motion> when parameterized by its variance. The real-space window is not a localized spherical top-hat, so its halo mass assignment needs a specified convention.
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