Accurate estimators of correlation functions in Fourier space

By E. Sefusatti, Martín Crocce, R. Scoccimarro, Hugh M. P. Couchman. 2015

185 citations recorded by the source corpus.

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% 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 datasets.

Subfields: Astronomy and Astrophysics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/acb37988303725e9b3063c824ae176527b21fa2a

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Citations in the corpus

nbodykit: An Open-source, Massively Parallel Toolkit for Large-scale Structure (2017, methodology): “13 https://pywavelets.readthedocs.io Figure 2 confirms the results of Sefusatti et al. (2016)—the interlacing technique performs very well at reducing the effects of aliasing on the measured power spectrum.”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Fourier space (2016, methodology): “The set-up of our grid implies a Nyquist frequency of kNy = 0.6 h Mpc−1, twice as large as the largest scale used in our analysis (kmax = 0.3 h Mpc−1) and the expected error on the power spectrum monopole at k = 0.3 h Mpc−1 due to aliasing is <0.1 per cent (Sefusatti et al. 2016).”
The Quijote Simulations (2019, methodology): “We use a Fast Fourier Transform (FFT) based estimator similar to the estimators described in Sefusatti & Scoccimarro (2005), Scoccimarro (2015), and Sefusatti et al. (2016).”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in Fourier space (2016, methodology): “In this work, we follow Sefusatti et al. (2016) and use the PCS interpolation to calculate the overdensity field on the grid, which is equivalent to convolving the underlying overdensity field with the following window function Wρ(s) in the configuration space, Wρ(s) = ⎧⎪⎨⎪⎩ 1 6 (4 − 6s2 + 3|s”
The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: First measurement of baryon acoustic oscillations between redshift 0.8 and 2.2 (2017, methodology): “In particular, Sefusatti et al. (2016) found that when a two-step interlacing was combined with a PCS interpolation, the effect of aliasing was reduced to a level below 0.1 per cent, even at the Nyquist scale.”
The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from the anisotropic power spectrum of the quasar sample between redshift 0.8 and 2.2 (2020, methodology): “Then, the F`(k) term can be computed with a Fast Fourier Transform, and the interlacing technique is used to reduce the effect of aliasing (Sefusatti et al. 2016).”