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We describe a class of observational strategies for probing the anisotropies in the cosmic microwave background (CMB) where the instrument scans on rings which can be combined into an n-torus, the {em ring torus}. This class has the remarkable property that it allows exact maximum likelihood power spectrum estimation in of order $N^2$ operations (if the size of the data set is $N$) under circumstances which would previously have made this analysis intractable: correlated receiver noise, arbitrary asymmetric beam shapes and far side lobes, non-uniform distribution of integration time on the sky and partial sky coverage. This ease of computation gives us an important theoretical tool for understanding the impact of instrumental effects on CMB observables and hence for the design and analysis of the CMB observations of the future. There are members of this class which closely approximate the MAP and Planck satellite missions. We present a numerical example where we apply our ring torus methods to a simulated data set from a CMB mission covering a 20 degree patch on the sky to compute the maximum likelihood estimate of the power spectrum $C_ell$ with unprecedented efficiency.
The cosmic microwave background (CMB) power spectrum is a powerful cosmological probe as it entails almost all the statistical information of the CMB perturbations. Having access to only one sky, the CMB power spectrum measured by our experiments is
Observations of the Cosmic Microwave Background (CMB) provide increasingly accurate information about the structure of the Universe at the recombination epoch. Most of this information is encoded in the angular power spectrum of the CMB. The aim of t
We describe and implement an exact, flexible, and computationally efficient algorithm for joint component separation and CMB power spectrum estimation, building on a Gibbs sampling framework. Two essential new features are 1) conditional sampling of
We present two novel methods for the estimation of the angular power spectrum of cosmic microwave background (CMB) anisotropies. We assume an absolute CMB experiment with arbitrary asymmetric beams and arbitrary sky coverage. The methods differ from
We have simulated the interferometric observation of the Cosmic Microwave Background (CMB) temperature and polarization fluctuations. We have constructed data pipelines from the time-ordered raw visibility samples to the CMB power spectra which utili