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AD 2000 - From Simulation to Optimization
June 19-23, 2000
INRIA Sophia Antipolis
Sophia Antipolis, France

Organizers
George Corliss, Christele Faure, Andre Galligo, Andreas Griewank, Laurent Hascoet, Uwe Naumann

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Numerical Differentiation Using Wavelets
by
Francois Chaplais
Ecole des Mines de Paris

The approximation conditions of Strang and Fix are first recalled. An elementary result on the differentiation of a finite elements approximation is proved, followed by a result by Lemarié on the differentiation of a wavelet decomposition. Daubechies' spline example is detailed.

The related algorithms are implemented as a Simulink toolbox. Examples of differentiating noisy signals are presented, using soft and hard wavelet thresholding.

http://cas.ensmp.fr/~chaplais/FTP/Mathematical_Notes/WaveletDiff.pdf

Date received: February 11, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cads-63.