Correcting for the Alias Effect When Measuring the Power Spectrum Using a Fast Fourier Transform

By Yipeng Jing. 2004

204 citations recorded by the source corpus.

Because of mass assignment onto grid points in the measurement of the power spectrum using a fast Fourier transform (FFT), the raw power spectrum ⟨|δf(k)|2⟩ estimated with the FFT is not the same as the true power spectrum P(k). In this paper we derive a formula that relates ⟨|δf(k)|2⟩ to P(k). For a sample of N discrete objects, the formula reads ⟨|δf(k)|2⟩ = [|W( + 2kN)|2P( + 2kN) + 1/N|W( + 2kN)|2], where W(k) is the Fourier transform of the mass assignment function W(r), kN is the Nyquist wavenumber, and n is an integer vector. The formula is different from that in some previous works in which the summation over n is neglected. For the nearest grid point, cloud-in-cell, and triangular-shaped cloud assignment functions, we show that the shot-noise term |W( + 2kN)|2 can be expressed by simple analytical functions. To reconstruct P(k) from the alias sum |W( + 2kN)|2P( + 2kN), we propose an iterative method. We test the method by applying it to an N-body simulation sample and show that the method can successfully recover P(k). The discussion is further generalized to samples with observational selection effects.

Subfields: Artificial Intelligence, Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2e820833509677c6cd2f090c214c28bfed090e42

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Citations in the corpus

THE LARGE-SCALE BIAS OF DARK MATTER HALOS: NUMERICAL CALIBRATION AND MODEL TESTS (2010, methodology): “Aliasing due to the cloud-in-cell grid is removed through the deconvolution technique outlined in Jing (2005).”
Multi-scale initial conditions for cosmological simulations (2011, methodology): “No deconvolution with the grid assignment operator was performed so that the CIC assignment leads to attenuation close to the Nyquist frequency of the mesh (outside of the plot) used to compute power spectrum in all cases (Jing 2005).”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Fourier space (2016, methodology): “We employ a triangular-shaped cloud method to assign galaxies to the 3D grid and correct for the aliasing effect following Jing (2005).”
Initial Conditions to Cosmological N-Body Simulations, or, How to Run an Ensemble of Simulations (2005, methodology): “When measuring power spectra of N-body simulations, the Poisson noise contribution is sometimes subtracted to arrive at a more ‘‘true’’ power spectrum that represents the underlying continuous density field (e.g., Smith et al. 2003; Jing 2005).”
Accurate estimators of correlation functions in Fourier space (2015, methodology): “Other approaches to limit aliasing effects in the estimation of the power spectrum as the one proposed by Jing (2005) cannot be easily extended to higher-order correlation functions.”
The detectability of baryonic acoustic oscillations in future galaxy surveys. (2007, methodology): “The degree of modification and the precise wavenumber above which the power spectrum is distorted depend upon the choice of assignment scheme (Hatton 1999; Jing 2005).”
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, background): “Additionally, each of these interpolation schemes has an associated grid correction factor that has to be applied to the overdensity field in Fourier space (Jing 2005).”
An improved SPH scheme for cosmological simulations (2015, background): “However, the accurate estimation of the velocity power spectrum of a particle distribution close to the Nyqvist frequency is non-trivial, because of aliasing of the velocity power by the binning kernel (see discussions in Jing 2005; Cui et al. 2008; Jasche, Kitaura & Ensslin 2009).”
The Influence of Baryons on the Clustering of Matter and Weak-Lensing Surveys (2005, methodology): “Clustering in the Nonradiative Run We measure the mass power spectrumP(k) for matter, gas, and stars separately, as well as for the total matter density in the simulations using the method of Jing (2005).”
The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9 (2011, background): “…the catalogue in cells using nearest grid point assignment ensuring that the Nyquist frequencies in each direction were much higher than the Fourier wavenumbers of interest (we corrected the power spectrum measurement for the small bias introduced by this gridding using the method of Jing 2005).”
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): “The higher order it is, the less level of aliasing survives after the correction (Jing 2005; Sefusatti et al. 2016).”
Cosmology with massive neutrinos I: towards a realistic modeling of the relation between matter, haloes and galaxies (2013, methodology): “We correct for the CIC mass assignment scheme as [53, 54]:”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the power spectrum and bispectrum of the DR12 BOSS galaxies (2016, methodology): “We apply the Cloud-inCells scheme (CiC) to associate galaxies to grid-cells and we apply the corresponding grid-deconvolution correction once the FT is performed (Jing 2005).”
Matter power spectrum and the challenge of percent accuracy (2015, unknown): “The measurement of the power spectrum with different mass assignment and aliasing correction schemes has also been subject to detailed investigation (Jing 2005; Cui et al. 2008).”