Accurate estimators of correlation functions in Fourier space

E. Sefusatti, M. Crocce, R. Scoccimarro, H. M P Couchman

    Research output: Contribution to journalArticle

    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 languageEnglish (US)
    Pages (from-to)3624-3636
    Number of pages13
    JournalMonthly Notices of the Royal Astronomical Society
    Volume460
    Issue number4
    DOIs
    StatePublished - Aug 21 2016

    Fingerprint

    estimators
    Fourier transform
    interpolation
    grids
    perturbation
    power spectra
    statistics
    Nyquist frequencies
    sampling
    estimates
    coefficients
    cells

    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

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

    In: Monthly Notices of the Royal Astronomical Society, Vol. 460, No. 4, 21.08.2016, p. 3624-3636.

    Research output: Contribution to journalArticle

    Sefusatti, E, Crocce, M, Scoccimarro, R & Couchman, HMP 2016, 'Accurate estimators of correlation functions in Fourier space', Monthly Notices of the Royal Astronomical Society, vol. 460, no. 4, pp. 3624-3636. https://doi.org/10.1093/mnras/stw1229
    Sefusatti, E. ; Crocce, M. ; Scoccimarro, R. ; Couchman, H. M P. / Accurate estimators of correlation functions in Fourier space. In: Monthly Notices of the Royal Astronomical Society. 2016 ; Vol. 460, No. 4. pp. 3624-3636.
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