Accelerating the 2-point and 3-point galaxy correlation functions using Fourier transforms

Understand

Though Fourier Transforms (FTs) are a common technique for finding correlation functions, they are not typically used in computations of the anisotropy of the two-point correlation function (2PCF) about the line of sight in wide-angle surveys because the line-of-sight direction is not constant on the Cartesian grid.

• Here we show how FTs can be used to compute the multipole moments of the anisotropic 2PCF.
• We also show how FTs can be used to accelerate the 3PCF algorithm of Slepian & Eisenstein (2015).
• In both cases, these FT methods allow one to avoid the computational cost of pair counting, which scales as the square of the number density of objects in the survey.