  The Large Area Telescope (LAT) onboard the Fermi satellite is observing the
gamma-ray sky in the high energy region, above 20 MeV. We have developed a
method to reconstruct the energy spectra of the gamma-rays detected by the
Fermi LAT instrument based on a Bayesian unfolding approach, that takes into
account the energy dispersion introduced by the instrument response. The method
has been successfully applied to reconstruct the energy spectra of both steady
and pulsating point sources. The analysis technique will be illustrated and the
results obtained in some significant test cases will be discussed.
