Accurate estimators of correlation functions in Fourier space
Abstract
Efficient estimators of Fourierspace statistics for large number of objects rely on fast Fourier transforms (FFTs), which are affected by aliasing from unresolved smallscale modes due to the finite FFT grid. Aliasing takes the form of a sum over images, each of them corresponding to the Fourier content displaced by increasing multiples of the sampling frequency of the grid. These spurious contributions limit the accuracy in the estimation of Fourierspace statistics, and are typically ameliorated by simultaneously increasing grid size and discarding highfrequency modes. This results in inefficient estimates for e.g. the power spectrum when desired systematic biases are well under per cent level. We show that using interlaced grids removes odd images, which include the dominant contribution to aliasing. In addition, we discuss the choice of interpolation kernel used to define density perturbations on the FFT grid and demonstrate that using higher order interpolation kernels than the standard CloudInCell algorithm results in significant reduction of the remaining images. We show that combining fourthorder interpolation with interlacing gives very accurate Fourier amplitudes and phases of density perturbations. This results in power spectrum and bispectrum estimates that have systematic biases below 0.01 per cent all the way to the Nyquist frequency of the grid, thus maximizing the use of unbiased Fourier coefficients for a given grid size and greatly reducing systematics for applications to large cosmological data sets.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 August 2016
 DOI:
 10.1093/mnras/stw1229
 arXiv:
 arXiv:1512.07295
 Bibcode:
 2016MNRAS.460.3624S
 Keywords:

 methods: analytical;
 methods: data analysis;
 methods: numerical;
 methods: statistical;
 largescale structure of Universe;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 13 pages, 9 figures. Section 3.1 expanded and 1 figure added to match the published version. Added link to software distribution