Accurate power spectrum estimation toward Nyquist limit

Abstract

The power spectrum, as a statistic in Fourier space, is commonly numerically calculated using the fast Fourier transform method to efficiently reduce the computational costs. To alleviate the systematic bias known as aliasing due to the insufficient sampling, the interlacing technique was proposed. We derive the analytical form of the shot noise under the interlacing technique, which enables the exact separation of the Poisson shot noise from the signal in this case. Thanks to the accurate shot noise subtraction, we demonstrate an enhancement in the accuracy of power spectrum estimation. For the three dark matter samples with number density ranging from 10-2 Mpc-3 h3 to 10-4 Mpc-3 h3 analyzed on a coarse mesh of size 3 h-1 Mpc with Cloud-in-Cell mass assignment scheme, the systematic bias is well under control up to the Nyquist frequency. On the contrary, the bias induced by the estimator that ignore the aliasing on the shot noise typically exceeds the statistical uncertainty on the frequency beyond 0.85 times the Nyquist frequency. The good performance of our estimation allows an abatement in the computational cost by using low resolution and low order mass assignment scheme in the analysis for huge surveys and mocks.