 3.
Ladyzhenskaya-Vorlesung Leipzig
Ingrid Daubechies
(Department of Mathematics and Program in Applied and Computational Mathematics - Princeton University)
"Mathematical problems suggested by Analog-to-Digital conversion"
am 16. October 2008, 16.00 Uhr c.t., Felix Klein Hörsaal, Mathematisches Institut, Johannisgasse 26, 04103 Leipzig
Kaffee um 15.30 Uhr im Raum I-43
Plakat - Fotos
ABSTRACT: In Analog-to-Digital conversion, continuously varying functions (e.g. the output of a microphone) are transformed into digital sequences from which one then hopes to be able to reconstruct a close approximation to the original function. The functions under consideration are typically band-limited (i.e. their Fourier transform is zero for frequencies higher than some given value, called the bandwidth); such functions are completely determined by samples taken at a rate determined by their bandwidth. These samples then have to be approximated by a finite binary representation. Surprisingly, in many practical applications one does not just replace each sample by a truncated binary expansion; for various technical reasons, it is more attractive to sample much more often and to replace each sample by just 1 or -1, chosen judicously. In this talk, we shall see what the attractions are of this quantization scheme, and discuss several interesting mathematical questions suggested by this approach. This will be a review of work by many others as well as myself. It is also a case study of how continuous interaction with engineers helped to shape and change the problems as we tried to make them more precise. |
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Professor Ingrid Daubechies hat wichtige Beiträge zur reinen und angewandten Mathematik gemacht, insbesondere in
harmonischer Analysis und Approximationstheorie. Die Daubechies Wavelets sind heute aus der angewandten Mathematik und der
Ingenieurwissenschaften nicht mehr weg zu denken.
In 2000 erhielt sie in Anerkennung ihrer Arbeit den Preis für Mathematik der National Academy of Sciences (NAS).
Mehr über sie hier |
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