paper

Correcting for the alias effect when measuring the power spectrum using FFT

arXiv:astro-ph/0409240 · doi:10.1086/427087

Abstract

Because of mass assignment onto grid points in the measurement of the power spectrum using the Fast Fourier Transform (FFT), the raw power spectrum $\la |δ^f(k)|^2\ra$ estimated with FFT is not the same as the true power spectrum . In this paper, we derive the formula which relates $\la |δ^f(k)|^2\ra$ to . For a sample of discrete objects, the formula reads: $\la |δ^f(k)|^2\ra=\sum_{\vec n} [|W(\kalias)|^2P(\kalias)+1/N|W(\kalias)|^2]$, where is the Fourier transform of the mass assignment function , is the Nyquist wavenumber, and is an integer vector. The formula is different from that in some of previous works where the summation over is neglected. For the NGP, CIC and TSC assignment functions, we show that the shot noise term $\sum_{\vec n} 1/N|W(\kalias)|^2]$ can be expressed by simple analytical functions. To reconstruct from the alias sum $\sum_{\vec n}|W(\kalias)|^2 P(\kalias)$, 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 . The discussion is further generalized to samples with observational selection effects.

12 pages, 2 figures; accepted for publication in ApJ

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