Abstract

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.