### Abstract

Efficient estimators of Fourier-space statistics for large number of objects rely on fast Fourier transforms (FFTs), which are affected by aliasing from unresolved small-scale 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 Fourier-space statistics, and are typically ameliorated by simultaneously increasing grid size and discarding high-frequency 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 Cloud-In-Cell algorithm results in significant reduction of the remaining images. We show that combining fourth-order 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.

Original language | English (US) |
---|---|

Pages (from-to) | 3624-3636 |

Number of pages | 13 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 460 |

Issue number | 4 |

DOIs | |

State | Published - Aug 21 2016 |

### Fingerprint

### Keywords

- Large-scale structure of Universe
- Methods: analytical
- Methods: data analysis
- Methods: numerical
- Methods: statistical

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Monthly Notices of the Royal Astronomical Society*,

*460*(4), 3624-3636. https://doi.org/10.1093/mnras/stw1229

**Accurate estimators of correlation functions in Fourier space.** / Sefusatti, E.; Crocce, M.; Scoccimarro, R.; Couchman, H. M P.

Research output: Contribution to journal › Article

*Monthly Notices of the Royal Astronomical Society*, vol. 460, no. 4, pp. 3624-3636. https://doi.org/10.1093/mnras/stw1229

}

TY - JOUR

T1 - Accurate estimators of correlation functions in Fourier space

AU - Sefusatti, E.

AU - Crocce, M.

AU - Scoccimarro, R.

AU - Couchman, H. M P

PY - 2016/8/21

Y1 - 2016/8/21

N2 - Efficient estimators of Fourier-space statistics for large number of objects rely on fast Fourier transforms (FFTs), which are affected by aliasing from unresolved small-scale 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 Fourier-space statistics, and are typically ameliorated by simultaneously increasing grid size and discarding high-frequency 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 Cloud-In-Cell algorithm results in significant reduction of the remaining images. We show that combining fourth-order 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.

AB - Efficient estimators of Fourier-space statistics for large number of objects rely on fast Fourier transforms (FFTs), which are affected by aliasing from unresolved small-scale 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 Fourier-space statistics, and are typically ameliorated by simultaneously increasing grid size and discarding high-frequency 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 Cloud-In-Cell algorithm results in significant reduction of the remaining images. We show that combining fourth-order 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.

KW - Large-scale structure of Universe

KW - Methods: analytical

KW - Methods: data analysis

KW - Methods: numerical

KW - Methods: statistical

UR - http://www.scopus.com/inward/record.url?scp=84980329197&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84980329197&partnerID=8YFLogxK

U2 - 10.1093/mnras/stw1229

DO - 10.1093/mnras/stw1229

M3 - Article

AN - SCOPUS:84980329197

VL - 460

SP - 3624

EP - 3636

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 4

ER -