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About: Wavelets, Splines, and the Reproduction of Polynomials

Module by: Rebecca Willett. E-mail the author

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Metadata

Name: Wavelets, Splines, and the Reproduction of Polynomials
ID: m11123
Language: English (en)
Summary: On well-known property of valid scaling functions in wavelet analysis is that the scaling functions can perfectly reproduce a polynomial of degree no more than the wavelet smoothness. This property can be easily derived using the Unser-Blu Scaling Function / Spline Factorization Theorem.
Subject: Mathematics and Statistics, Science and Technology
Keywords: wavelets, B-spline, vanishing moments, polynomials, basis
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
License: Creative Commons Attribution License CC-BY 1.0

Authors: Rebecca Willett (rebecca.willett@ieee.org)
Copyright Holders: Rebecca Willett (rebecca.willett@ieee.org)
Maintainers: Alena Scott (oetting@stat.rice.edu), Sujesh Sreedharan (sujesh@rice.edu), Rebecca Willett (rebecca.willett@ieee.org), Adan Galvan (agalvan@gmail.com), Charlet Reedstrom (charletr@gmail.com)

Latest version: 2.3 (history)
First publication date: Apr 23, 2003 12:00 am -0500
Last revision to module: Jun 7, 2005 3:43 pm -0500

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Version History

Version: 2.3 Jun 7, 2005 3:43 pm -0500 by Elizabeth Gregory
Changes:
Updated from CNXML 0.4 to CNXML 0.5

Version: 2.2 May 1, 2003 12:00 am -0500 by Rebecca Willett
Changes:
Moved content to factorization theorem page. This is now depricated.

Version: 2.1 Apr 23, 2003 12:00 am -0500 by Rebecca Willett
Changes:
Added connexions.

Version: 2.0 Apr 23, 2003 12:00 am -0500 by Rebecca Willett
Changes:
Initial module submission.

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  • the title of the work: Wavelets, Splines, and the Reproduction of Polynomials
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How to Cite and Attribute This Content

The following citation styles comply with the attribution requirements for the license (CC-BY 1.0) of this work:

American Chemical Society (ACS) Style Guide:

Willett, R. Wavelets, Splines, and the Reproduction of Polynomials, OpenStax_CNX Web site. http://cnx.org/content/m11123/2.3/, Jun 7, 2005.

American Medical Assocation (AMA) Manual of Style:

Willett R. Wavelets, Splines, and the Reproduction of Polynomials [OpenStax_CNX Web site]. June 7, 2005. Available at: http://cnx.org/content/m11123/2.3/.

American Psychological Assocation (APA) Publication Manual:

Willett, R. (2005, June 7). Wavelets, Splines, and the Reproduction of Polynomials. Retrieved from the OpenStax_CNX Web site: http://cnx.org/content/m11123/2.3/

Chicago Manual of Style (Bibliography):

Willett, Rebecca. "Wavelets, Splines, and the Reproduction of Polynomials." OpenStax_CNX. June 7, 2005. http://cnx.org/content/m11123/2.3/.

Chicago Manual of Style (Note):

Rebecca Willett, "Wavelets, Splines, and the Reproduction of Polynomials," OpenStax_CNX, June 7, 2005, http://cnx.org/content/m11123/2.3/.

Chicago Manual of Style (Reference, in Author-Date style):

Willett, R. 2005. Wavelets, Splines, and the Reproduction of Polynomials. OpenStax_CNX, June 7, 2005. http://cnx.org/content/m11123/2.3/.

Modern Languages Association (MLA) Style Manual:

Willett, Rebecca. Wavelets, Splines, and the Reproduction of Polynomials. OpenStax_CNX. 7 June 2005 <http://cnx.org/content/m11123/2.3/>.