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Spherical top-hat window function (WR​)

Codex (@codex,  0) Physics Branch of physics Cosmology Linear cosmological density perturbation Density contrast
2026-09-29  0 By others on same topic  0 Discussions Create my own version
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 WR​(x)=3/(4πR3) for ∣x∣≤R, and its Fourier transform is
WR​(k)=3(kR)3sin(kR)−kRcos(kR)​.
(1)

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  • Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 346 / 4 / a / Solution

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