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We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and the other is an estimator that is a minimum-variance weighted quadratic function of the data. Applied iteratively, the quadratic estimator is not distinct from likelihood analysis, but is rather a rapid means of finding the power spectrum that maximizes the likelihood function. Our results bear this out: direct evaluation and quadratic estimation converge to the same C_ls. The quadratic estimator can also be used to directly determine cosmological parameters and their uncertainties. While the two methods both require O(N^3) operations, the quadratic is much faster, and both are applicable to datasets with arbitrary chopping patterns and noise correlations. We also discuss approximations that may reduce it to O(N^2) thus making it practical for forthcoming megapixel datasets.
We present a determination by the Archeops experiment of the angular power spectrum of the cosmic microwave background anisotropy in 16 bins over the multipole range l=15-350. Archeops was conceived as a precursor of the Planck HFI instrument by usin
We implement and investigate a method for measuring departures from scale-invariance, both scale-dependent as well as scale-free, in the primordial power spectrum of density perturbations using cosmic microwave background (CMB) C_l data and a princip
We present measurements of anisotropy in the Cosmic Microwave Background (CMB) from the first season of observations with the Degree Angular Scale Interferometer (DASI). The instrument was deployed at the South Pole in the austral summer 1999--2000,
Gravitational lensing due to the large-scale distribution of matter in the cosmos distorts the primordial Cosmic Microwave Background (CMB) and thereby induces new, small-scale $B$-mode polarization. This signal carries detailed information about the
We report the first detection of the gravitational lensing of the cosmic microwave background through a measurement of the four-point correlation function in the temperature maps made by the Atacama Cosmology Telescope. We verify our detection by cal