We will indicate how important the ABSTRACT, means CONCEPTUAL point of view is, when it comes to develop efficient numerical algorithms for applications in the area of signal and image processing, wireless communication and related fields. Using the concept of locally compact Abelian GROUPS one can have a unified approach to continuous and discrete, to periodic and non-periodic, or one- and multidimensional functions.

We will describe, how this abstract view-point helps to obtain a unified description of Gabor Analysis, i.e. the decomposition of signals into building blocks obtained from a particular building block (Gabor atom) and its time-frequency shifts along some lattice in the so-called time-frequency plane (also called phase space).

At the end we hope to be able to provide a short description of a generalized function setting which is just the right tool for the development of appropriate concepts, which at the end help to reduce a continuous problem to a computationally feasible, finite-dimensional problem, where modern methods from numerical linear algebra can be used. In short, we will comment on the question: How does Gabor Analysis - performed with the help of MATLAB on a computer - help us to get a better understanding of Gabor analysis on the real line or on Euclidean spaces.