A very reasonable way to do ``Fourier Analysis'' if functions which are not periodic is to view them as a collection of local pieces, each of which can undergo a local Fourier analysis, instead of viewing it as a periodic function with ``infinite'' period. Time-frequency Analysis (TFA) is - an a certain sense - the theory of functions or distributions based on such a local Fourier analysis, formally realized by the Short-Time (or sliding window) Fourier transform (STFT). It is comparable to the continuous wavelet transform (STFT).

Within TF-analysis Gabor Analysis is concerned with the question, to which extent a sampled STFT still allows reconstruction of the signal, and which function spaces can be characterized (and how) by the behaviour of the (non-unique!!) coefficients. This leads to the so-called Modulation Spaces (comparable with the family of Besov spaces). Many operators, among them various pseudo-differential operator can be well described by their behaviour on these spaces. Gabor multipliers (or Anti-Wick operators) are a special class, related to slowly varying channels in mobile communication.

In this talk we plan to give a survey/introduction to the field, with some illustrations making use of the NuHAG collection of Gabor routines based on MATLAB.