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

We present a pair of related techniques to measure the two-point correlation function and the power spectrum with edge correction in any number of spatial dimensions. The underlying algorithm achieves unprecedented speed by using fast Fourier transforms for calculating a heuristically weighted, edge-corrected estimator for the two-point function. With its N log N scaling, it will be able to keep up with the expected exponential increase in astronomical data. Such a speedup is especially important for massive Monte Carlo studies with large data sets. In addition, we present a new method to estimate the power spectrum by means of numerical integration of the Hankel transform of the measur ed two-point correlation function. Stability and accuracy are ensured by a novel numerical technique based on Gauss-Bessel quadrature and double exponential transformation. The resulting edge-corrected estimator for the power spectrum reduces the smearing effect of the survey window function. The increased resolution will help to better constrain the shape of the power spectrum, such as features arising from baryonic oscillations.