= Top-hat filter
{wiki}
A \b[<top-hat filter>] smooths a field by averaging uniformly inside a chosen ball and assigning zero weight outside. For <radius> $R$, its normalized three-dimensional real-space weight is $W_R=3/(4\pi R^3)$ inside the ball. Applying it to the <density contrast> gives the overdensity on that scale and its <variance>. For uniform background density $\bar\rho$, the associated <mass> is $M=(4\pi/3)\bar\rho R^3$. A real-space top-hat differs from a <sharp-k smoothing filter>.
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