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The method computes an analytical estimate of the cross-correlation matrix directly from the data avoiding any Monte Carlo simulations. This allows to include naturally the mode coupling in this matrix. Further, this permits the computation of analytical error bars which are very compatible with those obtained from simulations (see [Tristram et al. 2005a](#xspect) for the temperature case). Because of the above, this method can be applied without modification to the estimation of the power spectrum of the correlated signal between a set of maps of the sky coming from multiple instruments with potentially different sky coverages. This method has been used on *Archeops* data to estimate the CMB angular power spectrum [Tristram et al. 2005b](#archeops_cl2) and the polarized foreground emission at the sub-millimeter and millimeter wavelength in [Ponthieu et al. 2005](#archeops_polar).
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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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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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<img name="image1" src="https://gitlab.in2p3.fr/tristram/Xpol/uploads/ee26c49f028906fbae336d882c506e91/image1.png" width=500px">
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<img name="image1" src="https://gitlab.in2p3.fr/tristram/Xpol/uploads/ee26c49f028906fbae336d882c506e91/image1.png" width="500px">
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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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* <a name="archeops_polar"> [Ponthieu et al. 2005] Ponthieu N. et al., 2005 A&A 444 327</a>
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* <a name="xspect"> [Tristram et al. 2005a] Tristram M. et al., 2005 MNRAS 358 833</a>
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* <a name="archeops_cl2"> [Tristram et al. 2005b] Tristram M. et al., 2005 A&A 436 785</a>
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* <a name="angularmomentum"> [Varshalovich et al. 1988] Varshalovich D. A., Moskalev A. N., Khersonoskii V. K., 1988, ''Quantum theory of Angular Momentum'', World Scientific, Singapore. </a>
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* <a name="angularmomentum"> [Varshalovich et al. 1988] Varshalovich D. A., Moskalev A. N., Khersonoskii V. K., 1988, ''Quantum theory of Angular Momentum'', World Scientific, Singapore. </a> |
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