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<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
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http://mathurl.com/render.cgi?E%20%3D%20mc%20%5E%202%5Cnocache
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# Xpol : a Power Spectrum estimator based on cross correlation between maps.
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*Xpol* is a method to estimate the polarized angular power spectra C<sub>l</sub>s by computing the cross-power spectra between a collection of input maps coming either from multiple detectors of the same experiment or from different instruments. The `pseudo' cross-power spectra are explicitly corrected for incomplete sky coverage, beam smoothing, filtering and pixelization. Assuming no correlation between the noise contribution from two different maps, each of the corrected cross-power spectra is an unbiased estimate of the C<sub>l</sub>s. Analytical error bars are derived for each of them. The cross-power spectra, that do not include the classical ''auto''-power spectra, are then combined using a Gaussian approximation of the likelihood function. This result can be compared to the auto-spectra for which the noise bias in multipole domain is requested as input.
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... | ... | @@ -14,7 +8,7 @@ The method computes an analytical estimate of the cross-correlation matrix direc |
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Generalizing MASTER equation for classical auto-spectra, we can compute the `pseudo' cross-power spectrum C<sub>l</sub>^X1xY2 between any two detectors
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%height=40px%Attach:image1.png
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![](image1.png)
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where
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* B<sub>l</sub> is the beam transfer function describing the beam smoothing effect which can be computed, for example via models and/or Monte Carlo signal-only simulations;
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