Numerical Questions in Time-frequency Analysis

By now Gabor analysis is a mature subfield of time-frequency analysis. It is well understood that for any lattice $\Lambda$ in the TF-plane the corresponding Gabor family $(\pi(\lambda)g)$ is a Gabor frame with good properties if the Gabor atom $g$ is a nice function, because the commutation properties of the frame operator $S$ imply that also the dual atom $\gd$ has good properties.

Parallel with an improved understanding of the functional analytic
properties of these non-orthogonal expansions (which in addition have some
built in redundancy, but also robustness) there are more and more efficient
methods which allow to provide in a fast way the minimal norm coefficients
for a given signal in an efficient way.

We plan to provide some insight into the questions, methods and algorithms
arising in this context. The demonstrations are all performed in a MATLAB
environment. Corresponding MATLAB files can be found on the NuHAG web-page
({\tt www.nuhag.eu}), including the LTFAT toolbox (Linear Time-Frequency
Toolbox), developed by Peter Soendergaard (presently at ARI = Acoustic
Research Institute, OEAW, Vienna).