Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42C40, 65T60, 11A55, 40A15

Retrieve articles in all journals with MSC (2000): 42C40, 65T60, 11A55, 40A15

Additional Information

Joel Glenn
Affiliation: Department of Mathematics and Computer Science, Colorado College, Colorado Springs, Colorado 80903

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia