Max Tegmark's library: power.ps
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A METHOD FOR EXTRACTING MAXIMUM RESOLUTION POWER SPECTRA
FROM GALAXY SURVEYS
Author: Max Tegmark
The power spectrum estimated from a galaxy redshift survey is the real
spectrum convolved with a window function, so when estimating the
power on very large scales (for small k),
it is important that this
window function be as narrow as possible. A method that achieves this
is presented. The optimal estimate of
P(k) is found to be the
Fourier transform of the number density fluctuations
weighted by a function psi, and the optimal psi
is found to
be the ground-state solution of the Schöodinger equation, with the
inverse selection function as the potential.
This quantum mechanics analogy occurs basically because we want the
weight function to be narrow both in Fourier space (to give a narrow
window) and in real space (to minimize the variance from shot noise).
An optimal method for averaging the estimates at different
also presented, generalizing the standard procedure of averaging over
shells in k-space.
Finally, a discrete version of the method is presented, dividing
space into ``fuzzy pixels", which has the advantage of being able to
handle redshift distortions in a straightforward way.
This site also contains the latest versions of two papers that are
referenced in the text;
Tegmark 1994 ("T94")
Tegmark & Bromley 1995.
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This page was last modified July 1, 1998.