  In this talk I propose the first fast methods which can analyze CMB data
taking into account correlated noise, arbitrary beam shapes, non-uniform
distribution of integration time on the sky, and partial sky coverage, without
the need for approximations. These ring torus methods work by performing the
analysis in the time ordered domain (TOD) rather than on the sky map of
fluctuations. They take advantage of the simplicity of noise correlations in
the TOD as well as certain properties of the group of rotations SO(3). These
properties single out a family of scanning strategies as favorable, namely
those which scan on rings and have the geometry of an n-torus. This family
includes the strategies due to TOPHAT, MAP and Planck. I first develop the
tools to model the time ordered signal, using Fast Fourier Transform methods
for convolution of two arbitrary functions on the sphere (Wandelt and G\'orski
2000). Then I apply these ideas to show that in the case of a 2-torus one can
reduce the time taken for CMB power spectrum analysis from an unfeasible order
N^3 to order N^2, where N ~ 10^5-10^8 is the number of resolution elements
(Wandelt and Hansen, in preparation).
