Effective beam window matrix introduced in Eq. (41) and detailed in Eq. (E.8a), for the cross-spectra of two simulated Planck maps discussed in Sect. 5. Left panel: raw elements of , showing for each ℓ how the measured XY map angular power spectrum is impacted by the input TT spectrum, because of the observation of the sky with the beams. Right panel: blown-up ratio of the non-diagonal elements to the diagonal ones: 100 W^XY,TT_ℓ/W^TT,TT_ℓ