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Optimally matched wavelets

  1. Henning Thielemann*

Article first published online: 22 DEC 2004

DOI: 10.1002/pamm.200410274

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PAMM

PAMM

Volume 4, Issue 1, pages 586–587, December 2004

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How to Cite

Thielemann, H. (2004), Optimally matched wavelets. Proc. Appl. Math. Mech., 4: 586–587. doi: 10.1002/pamm.200410274

Author Information

  1. Universität Bremen, FB 3, Zentrum für Technomathematik, PF 33 04 40, 28334 Bremen

*Phone: +49 - (0)421 218 9501 Fax: +49 - (0)421 218 9562

Publication History

  1. Issue published online: 22 DEC 2004
  2. Article first published online: 22 DEC 2004

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Abstract

Several applications require to retrieve a certain pattern from a signal where the actual scaling of the pattern is not known before. We consider applications like evaluation of mass spectrograms, detection of component wearout by observing the current of an engine, detection of pollutions of rotor spinning machines, decomposition of (audio) signals into time-frequency atoms.

We try to solve this problem with discrete wavelet transforms where the wavelet function is constructed to match the given pattern. An approach for a biorthogonal basis constructed by the lifting scheme is presented. This method is rather simple and fast and allows the choice of the smoothness at least of the primal wavelet in a very natural way. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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