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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A continued fraction analysis of periodic wavelet coefficients


Author: Joel Glenn
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1367-1375
MSC (2000): Primary 42C40, 65T60; Secondary 11A55, 40A15
Published electronically: December 22, 2003
MathSciNet review: 2053341
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Abstract: We define and prove the existence of crossings of wavelet coefficients translated by integer multiples of the numerator of a continued fraction convergent of the ratio of the sampling interval to the period of the wavelet coefficients. Crossings are found to be translation invariant $\pm 1$. Intervals between crossings are analyzed for wavelets with $n$ vanishing moments. These wavelets act as multiscale differential operators. These crossings reveal different locations in the period where there is equality in the $n$th derivative of an averaging of the signal. These results will be employed in the estimation of frequency components in future publications.


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Additional Information

Joel Glenn
Affiliation: Department of Mathematics and Computer Science, Colorado College, Colorado Springs, Colorado 80903
Email: jglenn@coloradocollege.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07064-3
PII: S 0002-9939(03)07064-3
Received by editor(s): February 19, 2002
Received by editor(s) in revised form: September 26, 2002
Published electronically: December 22, 2003
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society