Window effect in the power spectrum analysis of a galaxy redshift survey

TL;DR

This paper examines how the window function affects galaxy power spectrum analysis, comparing convolved and deconvolved methods, and applies these techniques to SDSS LRG data.

Contribution

It introduces and compares two approaches for handling window effects in galaxy power spectrum analysis, including a Fourier deconvolution method.

Findings

Demonstrates the impact of window function on multipole power spectrum.

Provides a practical method for deconvolving window effects from survey data.

Applies methods successfully to SDSS LRG sample.

Abstract

We investigate the effect of the window function on the multipole power spectrum in two different ways. First, we consider the convolved power spectrum including the window effect, which is obtained by following the familiar (FKP) method developed by Feldman, Kaiser and Peacock. We show how the convolved multipole power spectrum is related to the original power spectrum, using the multipole moments of the window function. Second, we investigate the deconvolved power spectrum, which is obtained by using the Fourier deconvolution theorem. In the second approach, we measure the multipole power spectrum deconvolved from the window effect. We demonstrate how to deal with the window effect in these two approaches, applying them to the Sloan Digital Sky Survey (SDSS) luminous red galaxy (LRG) sample.