Numerical Questions in Time-frequency AnalysisHans G. Feichtinger given at Austrian Numerics Days *Graz (12.04.13) id: 2502 length: min status: type: www: http://www.numerik.math.tugraz.at/tagungen/anaday13/ LINK-Presentation: https://nuhagphp.univie.ac.at/dateien/talks/2502_Anad13Fei.pdf ABSTRACT: 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). |