Fast Edge Corrected Measurement of the Two-Point Correlation Function and the Power Spectrum

Abstract

We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point function with an heuristically weighted edge corrected estimator. Once the correlation function is measured, we estimate the power spectrum via numerical integration of the Hankel transform connecting the two. We introduce an efficient numerical technique based on Gauss-Bessel-quadrature and double exponential transformation. This, combined with our, or any similar, two-point function estimator leads to a novel edge corrected estimator for power spectra. The pair of techniques presented are the Euclidean analogs of those developed and widely used in cosmic microwave background research for spherical maps.

4 pages, 2 figures, submitted to ApJL

References in corpus (11)

• Stable clustering, the halo model and nonlinear cosmological power spectra
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Evolution of structure in cold dark matter universes
• Uncorrelated Modes of the Nonlinear Power Spectrum
• Fast estimation of polarization power spectra using correlation functions
• Myths and Truths Concerning Estimation of Power Spectra
• Angular Clustering with Photometric Redshifts in the Sloan Digital Sky Survey: Bimodality in the Clustering Properties of Galaxies
• Wide Angle Redshift Distortions Revisited
• Fourier analysis of luminosity-dependent galaxy clustering
• Three-Point Statistics from a New Perspective
• Inverting the Angular Correlation Function

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