  We introduce new Fourier band-power estimators for cosmic shear data analysis
and E/B-mode separation. We consider both the case where one performs E/B-mode
separation and the case where one does not. The resulting estimators have
several nice properties which make them ideal for cosmic shear data analysis.
First, they can be written as linear combinations of the binned cosmic shear
correlation functions. Second, they account for the survey window function in
real-space. Third, they are unbiased by shape noise since they do not use
correlation function data at zero separation. Fourth, the band-power window
functions in Fourier space are compact and largely non-oscillatory. Fifth, they
can be used to construct band-power estimators with very efficient data
compression properties. In particular, we find that all of the information on
the parameters $\Omega_{m}$, $\sigma_{8}$ and $n_{s}$ in the shear correlation
functions in the range of $\sim10-400$ arcminutes for single tomographic bin
can be compressed into only three band-power estimates. Finally, we can achieve
these rates of data compression while excluding small-scale information where
the modeling of the shear correlation functions and power spectra is very
difficult. Given these desirable properties, these estimators will be very
useful for cosmic shear data analysis.
