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Abstract: abridged A method to rapidly estimate the Fourier power spectrum of a pointdistribution is presented. This method relies on a Taylor expansion of thetrigonometric functions. It yields the Fourier modes from a number of FFTs,which is controlled by the order N of the expansion and by the dimension D ofthe system. In three dimensions, for the practical value N=3, the number ofFFTs required is 20. We apply the method to the measurement of the powerspectrum of a periodic point distribution that is a local Poisson realizationof an underlying stationary field. We derive explicit analytic expression forthe spectrum, which allows us to quantify-and correct for-the biases inducedby discreteness and by the truncation of the Taylor expansion, and to bound theunknown effects of aliasing of the power spectrum. We show that these aliasingeffects decrease rapidly with the order N. The only remaining significantsource of errors is reduced to the unavoidable cosmic-sample variance due tothe finite size of the sample. The analytical calculations are successfullychecked against a cosmological N-body experiment. We also consider the initialconditions of this simulation, which correspond to a perturbed grid. Thisallows us to test a case where the local Poisson assumption is incorrect. Evenin that extreme situation, the third-order Fourier-Taylor estimator behaveswell. We also show how to reach arbitrarily large dynamic range in Fourierspace i.e., high wavenumber, while keeping statistical errors in control, byappropriately -folding- the particle distribution.

Autor: Stephane Colombi 1, Andrew H. Jaffe 2, Dmitri Novikov 2, Christophe Pichon 1 1 IAP, 2 Imperial College


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