Deconvolution of window effect in galaxy power spectrum analysis

TL;DR

This paper introduces a fast Fourier transform-based deconvolution method to correct for survey window effects in galaxy power spectrum analysis, improving measurement accuracy and covariance matrix properties.

Contribution

A novel deconvolution technique for galaxy power spectra that efficiently removes survey window effects using FFT and the deconvolution theorem.

Findings

Corrected power spectrum amplitudes.

Covariance matrices become nearly diagonal.

Enhanced BAO feature analysis.

Abstract

We develop a new method for deconvolving the smearing effect of the survey window in the analysis of the galaxy multipole power spectra from a redshift survey. This method is based on the deconvolution theorem, and is compatible with the use of the fast Fourier transform. It is possible to measure the multipole power spectra deconvolved from the window effect efficiently. Applying this method to the luminous red galaxy sample of the Sloan Digital Sky Survey data release 7 as well as mock catalogues, we demonstrate how the method works properly. Using this deconvolution technique, the amplitude of the multipole power spectrum is corrected. Besides, the covariance matrices of the deconvolved power spectra get quite close to the diagonal form. This is also advantageous in the study of the BAO signature.