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The high frequency behaviour of continuous wavelet transforms. (English) Zbl 0838.44004
Summary: The high frequency behaviour of continuous wavelet transforms is characterized by the number of vanishing moments of the corresponding basic wavelets. As a consequence we give satisfying answer to the following questions of theoretical as well as practical interest:
What are the differences or similarities between transforms to different wavelets?
Why do wavelet transforms react so sensitively to abrupt signal changes?

MSC:
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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