Gabor Analysis is a paritcular part of time frequency analysis. While time-frequency analysis treats signals by looking at their short-time (or sliding-window) Fourier transform, to achieve a time (or location) dependent Fourier analysis of the signal under consideration, the idea of D.Gabor was (alrady in 1946) that a discretized version of the continuous inversion formula, with Gaussian building blocks should allow for a unique representation of ``arbitrary signals''. Clearly enough the (hoped for) unique coefficients would indicate how much energy you find in a given musical signal at a given (discrete) time and a given (discrete) family of harmonic frequencies.

The mathematical theory has brought a fairly detailed understanding of the situation. I will present the basic parts of it, using linear algebra and some group theoretic arguments, which make certain algorithms work highly efficiently. Among other, we can now understand the action of Gabor multipliers quite well: these are operators, which are obtained by doing a pointwise multiplication of the (minimal norm) Gabor coefficients before resynthesis. All the results shown can be demonstrated using MATLAB code developed at or in cooperation with NuHAG.

See www.nuhag.eu and in particular
http://www.univie.ac.at/nuhag-php/mmodule/
for details