  We apply the Gabor transform methodology proposed in (Hansen et al. 2002,
2003) to the WMAP data in order to test the statistical properties of the CMB
fluctuation field and specifically to evaluate the fundamental assumption of
cosmological isotropy. We estimate the angular power spectrum locally in discs
of various sizes positioned in different directions. We determine whether the
spatial position of a few outliers in the angular power spectrum could suggest
the presence of residual foregrounds or systematic effects. For multipoles
close to the first peak, the most deviant local estimates from the best fit
WMAP model are associated with a few particular areas close to the Galactic
plane. Such deviations also include the ``dent'' in the spectrum just shortward
of the first peak which was remarked upon by the WMAP team. Estimating the
angular power spectrum excluding these areas gives a slightly higher first
Doppler peak amplitude. Finally, we probe the isotropy of the largest angular
scales by estimating the power spectrum on hemispheres and reconfirm strong
indications of a north-south asymmetry previously reported by other authors. We
find tentative evidence for residual foregrounds in the range l=2-4, which
could be associated with the low measured quadrupole amplitudes and other
anomalies on these angular scales. However, over the range l=5-40 the observed
asymmetry is much harder to explain in terms of residual foregrounds and known
systematic effects. Such asymmetric distributions of power on the sky provide a
serious test for the cosmological principle of isotropy.

Astrophysics