In this MATLAB-based presentation the author will explain how one can understand and illustrate the foundations of Gabor analysis with the help of MATLAB. From the point of view of Abstract Harmonic Analysis one works with functions over finite Abelian groups, hence linear operators can be represented by matrices and optimal estimates can be computed explicitely using matrix analysis methods. The fact that the algebraic structures are the same as in the continuous case, but with the advantage that all sums are finite, allows to destill (and check numerically) various identities in a concrete setting. MATLAB (or OCTAVE, or the LTFAT toolbox) also allow to carry out experiments in order to come up with conjectures or first ideas about possible claims in the continuous case.



Various talks on the subject can be found at

http://www.univie.ac.at/nuhag-php/nuhag_talks/

author = Feichtinger, title = Gabor