  We describe a connection between two seemingly different problems: (a) the
construction of projections in noncommutative tori, (b) the construction of
tight Gabor frames. The present investigation relies an interpretation of
projective modules over noncommutative tori in terms of Gabor analysis. The
main result demonstrates that Rieffel's condition on the existence of
projections in noncommutative tori is equivalent to the Wexler-Raz
biorthogonality relations for tight Gabor frames. Therefore we are able to
invoke results on the existence of Gabor frames in the construction of
projections in noncommutative tori. In particular, the projection associated
with a Gabor frame generated by a Gaussian turns out to be Boca's projection.
Our approach to Boca's projection allows us to characterize the range of
existence of Boca's projection. The presentation of our main result provides a
natural approach to the Wexler-Raz biorthogonality relations in terms of
Hilbert C*-modules over noncommutative tori.
