Noise weighting in CMB power spectrum estimation

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Rajib Saha
Posts: 1
Joined: March 23 2005
Affiliation: Indian Insitute of Technology, Kanpur, (visitor IUCAA)

Noise weighting in CMB power spectrum estimation

Post by Rajib Saha » March 24 2005

Hi


I am just starting to work on (beginning to explore) the estimation of CMB
power spectrum from the WMAP data I have a few questions on (inverse)
noise weighting used in the following WMAP paper "First year Wilkinson
Microwave Anisotropy Probe (WMAP) Observation: The angular power spectrum"
by Hinshaw et al. :

* Appendix A.
Each pixel is weighted according to W(p)=M(p)*N_obs(p) (Appendix A1.2)
Should there be a division by the average of the N_obs(p) also ? Otherwise
weights are large as N_obs is a large number for each pixel. Am I missing
something?


* What is the basic purpose of the noise weighting?

If I find power spectrum using a W(p)=M(p)*N_obs(p)/<N_obs(p) in the
relevant multipole range will it correct for some noise bias in the power
spectrum or it is done to get optimal error bars? I.e., should I expect
the estimated power spectrum to differ significantly when estimated with
or without noise weighting.

Also is this relevant when only cross correlations between channels are
being used. (Here the noise term drops out since it is uncorrelated
between channels.)

* I will appreciate if someone could point me to expository article where
I can get a discussion about the inverse noise weighting and other issues
of CMB power spectrum estimation.


Rajib Saha

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