Gabor analysis: MATLAB based experiments and mathematical theory
Hans G. Feichtinger
given at feit12 (19.04.12 15:30)
In this presentation I will demonstrate that done suitably one can use a mathematical software package like MATLAB (or OCTAVE) to do not only linear algebra on the computer, but also in order to develop heuristics, illustrate mathematical observations, and develop efficient algorithm using a combination of theory and actual computation. A few aspects of this general claim can be illustrated.
Mathematically Gabor analysis can be described as a local Fourier expansion of signals, as it is for example used by the MP3 audio compression algorithms (developed around 1992). A [musical] signal is decomposed in (overlapping) pieces, and each of those pieces is analyzed for its frequency content, comparable to a musical score. The mathematical theory can be linked to linear algebra, which in turn is illustrated/realized using MATLAB.