  Heisenberg modules over noncommutative tori may also be viewed as Gabor
frames. Building on this fact, we relate to deformations of noncommutative tori
a bundle of Banach spaces induced by Heisenberg modules. The construction of
this bundle of Banach spaces rests on deformation results of Gabor frames with
windows in Feichtinger's algebra due to Feichtinger and Kaiblinger. We extend
some of these results to Heisenberg modules, e.g. we establish an analog of the
results by Feichtinger-Kaiblinger and a Balian-Low theorem.
