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Optimally matched wavelets
Author(s) -
Thielemann Henning
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410274
Subject(s) - wavelet , biorthogonal system , spectrogram , algorithm , computer science , simple (philosophy) , smoothness , basis (linear algebra) , rotor (electric) , biorthogonal wavelet , signal (programming language) , function (biology) , lifting scheme , pattern recognition (psychology) , discrete wavelet transform , mathematics , artificial intelligence , wavelet transform , engineering , mathematical analysis , mechanical engineering , philosophy , geometry , epistemology , evolutionary biology , biology , programming language
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)