Fast quadratic power spectrum estimators and the E–B decomposition

We describe a fast, quadratic power spectrum estimator for cosmic microwave background polarization fields, based on heuristically-weighted correlation functions. The method can handle real-world effects such as inhomogeneous or correlated noise, and arbitrary sky cuts. A significant feature is that the electric and magnetic polarization powers are separated exactly in the mean, even for observations covering only a small region of the sky, and with a negligible increase in computational cost. The method is illustrated with simulations for a large-area survey, and a future, deep magnetic-polarization survey.