  The Fourier transform of a dataset apodised with a window function is known
as the Gabor transform. In this paper we extend the Gabor transform formalism
to the sphere with the intention of applying it to CMB data analysis. The Gabor
coefficients on the sphere known as the pseudo power spectrum is studied for
windows of different size. By assuming that the pseudo power spectrum
coefficients are Gaussian distributed, we formulate a likelihood ansatz using
these as input parameters to estimate the full sky power spectrum from a patch
on the sky. Since this likelihood can be calculated quickly without having to
invert huge matrices, this allows for fast power spectrum estimation. By using
the pseudo power spectrum from several patches on the sky together, the full
sky power spectrum can be estimated from full-sky or nearly full-sky
observations.
