While time-frequency analysis starts to play an increasingly important role in abstract analysis, e.g. in the context of pseudo-differential operators, or the modelling of mobile communication channels, it has also become a versatile tool for signal processing applications.

The problem concerns the (linear) representation of signals (also images) as superpositions of well structured, but non-orthogonal collections of building blocks. Such an approach requires considerations of numerical stability and use of memory as well as the use of efficient numerical linear algebra methods.

On the other hand it allows to produce intuitively appealing
images supporting intuition very much, and to run systematic
experiments, which was not possible in such a way just 25 years ago. Meanwhile extensive collections of MATLAB files are available from NuHAG resp. within the LTFAT toolbox of Peter Soendergaard.