  This paper considers generators of Heisenberg modules in the case of twisted
group $C^*$-algebras of closed subgroups of locally compact abelian groups and
how the restrction and/or periodization of these generators yield generators
for other Heisenberg modules. Since generators of Heisenberg modules are
exactly the generators of (multi-window) Gabor frames, our methods are going to
be from Gabor analy\-sis. In the latter setting the procedure of restriction
and periodization of generators is well known. Our results extend this
established part of Gabor analy\-sis to the general setting of locally compact
abelian groups. We give several concrete examples where we demonstrate some of
the consequences of our results. Finally, we show that vector bundles over an
irrational noncommutative torus may be approximated by vector bundles for
finite-dimensional matrix algebras that converge to the irrational
noncommutative torus with respect to the module norm of the generators, where
the matrix algebras converge in the quantum Gromov-Hausdorff distance to the
irrational noncommutative torus.
