In this talk we will show, that methods from conceptual (often called
abstract) Harmonic Analysis allow not only a unified view on problems
arising in theoretical physics (coherent states), but also lead to
efficient algorithms for signal processing applications. Arguments
from group representation theory allow the derivation of fundamental
identities which equally important for the understanding of Gabor
systems from a theoretical point of view as well as for numerical
computations over finite Abelian groups. Appropriate function spaces,
the so-called modulation spaces resp. the Segal algebra S0(G)
allow the analysis of operators (be it the Kohn-Nirenberg or the
Anti-Wick calculus), but are also well suited to study the
problem of approximating operators over Euclidean spaces by similar
operators over (sufficiently large) finite groups, which are
then accessible to actual computations.