  The angular power spectrum is a gauge-independent observable that is in
principle the natural tool for analysing galaxy number counts. In practice, the
problem is that the computational requirements for next-generation
spectroscopic surveys such as Euclid and the Square Kilometre Array are
currently unfeasible. We propose a new method to save computational time for
spectroscopic angular power spectra. This hybrid method is modelled on the
Fourier power spectrum approach of treating relatively thick redshift bins
(redshift width ~0.1) as separate surveys. In the hybrid method, each thick bin
is further subdivided into thin bins (redshift width ~0.01); all the
correlations within each thick bin are computed, while cross-bin correlations
beyond the thick bins are neglected. Constraints on cosmological parameters
from the hybrid method are comparable to those from the standard galaxy power
spectrum analysis - but they have the advantage that cosmic evolution,
wide-angle and lensing effects are naturally included, while no
Alcock-Paczynski correction is needed. The hybrid method delivers much tighter
constraints than a 2D tomographic approach that is typical for photometric
surveys, which considers only thick bins and the correlations between them.
Furthermore, for standard cosmological parameters our method is not biased by
neglecting the effects of lensing on number counts, while the tomographic
method is strongly biased.
