The application of noncommutative tori in signal analysis is discussed in
this talk.
I show that the Heisenberg modules over noncommutative tori are actually
Gabor
frames, well-known in time-frequency analysis. The generators of the
Heisenberg modules have been studied extensively but tools and results
from time-frequency analysis allows one to gain a better understanding of
their structure.
We present results based on the duality theorem between Gabor multi-window
frames and Riesz basis superframes, the density theorem, existence of
generators
in Feichtinger's algebra, construction of projections in noncommutative
tori using
Gabor frames.