Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-03-07064-3
Published electronically: December 22, 2003
MathSciNet review: 2053341
Full-text PDF

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?)

  • [1] C. Burrus, R. Gopinah, and H. Guo, Introduction to Wavelets and Wavelet Transforms: A Primer, Prentice-Hall, Inc., Upper Saddle River, New Jersey, 1998, pp. 190-195.
  • [2] W. LeVeque, Fundamentals of Number Theory, Addison-Wesley Publishing Company, Inc., 1977, pp. 232-237. MR 58:465
  • [3] S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, New York, 1998, pp. 169-171. MR 99m:94012
  • [4] Ya. Khintchine, Continued Fractions, P. Noordhoff Ltd., Groningen, 1963, pp. 11-12. MR 28:5038

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
Email: jglenn@coloradocollege.edu

DOI: https://doi.org/10.1090/S0002-9939-03-07064-3
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

American Mathematical Society