It is the purpose of this talk to present various
concepts from what is usually called "abstract
harmonic analysis" with the purpose of showing
how the essential ingredients of such a theory
helps to overcome technical problems usually
associated with Fourier analysis, time-frequency
analysis, e.g. Gabor analysis, sampling theory,
or computational harmonic analysis. A cornerstone
in the discussion will be the discussion how
a continuous Fourier transform (using integrals)
can be realized using mathematical software such
as MATLAB.