Mathematical Foundations of Gabor AnalysisHans G. Feichtinger given at Univ. Canterbury, Christchurch (29.07.10 15:10) id: 1930 length: 30min status: hide type: invited www: http://www.math.canterbury.ac.nz/seminars/#s100729 LINK-Presentation: https://nuhagphp.univie.ac.at/dateien/talks/1930_CanterburyTLK.pdf ABSTRACT: Gabor Analysis can be viewed as a sub-field of time-frequency analysis, which essentially is making use of a time-localized version of the Fourier transform, using a certain (localization) window. D.Gabor has suggest in 1946 to use the Gauss-function, due to its optimality property for the Heisenberg relation, and sample it over the integer lattice in TF-domain. We will give a summary of results obtained in the last 30 years concerning Gabor families, in particular (redundant) Gabor frames and Gabor Riesz bases, and will try to relate these findings to applied problems, e.g. in audio (MP3) and mobile communication, but also mention the role of so-called Banach frames, Gelfand triples for other branches of modern analysis. |