  Around 1980 Connes extended the notions of geometry to the non-commutative
setting. Since then {\it non-commutative geometry} has turned into a very
active area of mathematical research. As a first non-trivial example of a
non-commutative manifold Connes discussed subalgebras of rotation algebras, the
so-called {\it non-commutative tori}. In the last two decades researchers have
unrevealed the relevance of non-commutative tori in a variety of mathematical
and physical fields. In a recent paper we have pointed out that non-commutative
tori appear very naturally in Gabor analysis. In the present paper we show that
Janssen's result on good window classes in Gabor analysis has already been
proved in a completely different context and in a very disguised form by Connes
in 1980. Our treatment relies on non-commutative analogs of Wiener's lemma for
certain subalgebras of rotation algebras by Gr\"ochenig and Leinert.
