Measuring the Galaxy Power Spectrum with Future Redshift Surveys

Precision measurements of the galaxy power spectrum P(k) require a dataanalysis pipeline that is both fast enough to be computationally feasible andaccurate enough to take full advantage of high-quality data. We present arigorous discussion of different methods of power spectrum estimation, withemphasis on the traditional Fourier method, the linear (Karhunen-Loeve; KL),and quadratic data compression schemes, showing in what approximations theygive the same result. To improve speed, we show how many of the advantages ofKL data compression and power spectrum estimation may be achieved with acomputationally faster quadratic method. To improve accuracy, we deriveanalytic expressions for handling the integral constraint, since it is crucialthat finite volume effects are accurately corrected for on scales comparable tothe depth of the survey. We also show that for the KL and quadratic techniques,multiple constraints can be included via simple matrix operations, therebyrendering the results less sensitive to galactic extinction and mis-estimatesof the radial selection function. We present a data analysis pipeline that weargue does justice to the increases in both quality and quantity of data thatupcoming redshift surveys will provide. It uses three analysis techniques inconjunction: a traditional Fourier approach on small scales, a pixelizedquadratic matrix method on large scales and a pixelized KL eigenmode analysisto probe anisotropic effects such as redshift-space distortions.