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About: Existence and Convergence of Fourier Series

Module by: Michael Haag, Justin Romberg. E-mail the authors

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Name: Existence and Convergence of Fourier Series
ID: m10745
Language: English (en)
Summary: This module discusses the existence and covergence of the Fourier Series to show that it can be a very good approximation for all signals. The Dirichlet conditions, which are the sufficient conditions to guarantee existence and convergence of the Fourier series, are also discussed.
Subject: Science and Technology
Keywords: converge, convergence, dirichlet, dirichlet conditions, discontinuity, exist, existence, fourier, fourier coefficient, fourier series, pointwise, pointwise convergence, strong dirichlet conditions, weak dirichlet conditions
License: Creative Commons Attribution License CC-BY 1.0
Authors: Michael Haag (mjhaag@gmail.com), Justin Romberg (jrom@ece.gatech.edu)
Copyright Holders: Michael Haag (mjhaag@gmail.com), Justin Romberg (jrom@ece.gatech.edu)
Maintainers: Michael Haag (mjhaag@gmail.com), Justin Romberg (jrom@ece.gatech.edu), Richard Baraniuk (richb@rice.edu), Mariyah Poonawala (mariyah@rice.edu), Prashant Singh (prash@ece.rice.edu)
Latest version: 2.5 (history)
First publication date: Jul 18, 2002 12:00 am -0500
Last revision to module: Jul 29, 2010 2:38 pm -0500

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Version History

Version: 2.5 Jul 29, 2010 2:38 pm -0500 by Collins Williamson
Changes: 
2010 update
Version: 2.4 Sep 30, 2009 4:25 pm -0500 by Richard Baraniuk
Changes: 
added google analytics tracking code
Version: 2.3 Jun 22, 2005 8:09 pm -0500 by Charlet Reedstrom
Changes: 
update to cnxml-0.5, update mathml
Version: 2.2 Jul 9, 2003 2:05 pm -0500 by Charlet Reedstrom
Changes: 
addmaintainers
Version: 2.1 Jul 19, 2002 12:00 am -0500 by (Unknown)
Changes: 
New module created. Verified printing.
Version: 2.0 Jul 18, 2002 12:00 am -0500 by (Unknown)
Changes: 
Added initial template for new module m10745

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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:

Haag, M.; Romberg, J. Existence and Convergence of Fourier Series, Connexions Web site. http://cnx.org/content/m10745/2.5/, Jul 29, 2010.

American Medical Assocation (AMA) Manual of Style:

Haag M, Romberg J. Existence and Convergence of Fourier Series [Connexions Web site]. July 29, 2010. Available at: http://cnx.org/content/m10745/2.5/.

American Psychological Assocation (APA) Publication Manual:

Haag, M., & Romberg, J. (2010, July 29). Existence and Convergence of Fourier Series. Retrieved from the Connexions Web site: http://cnx.org/content/m10745/2.5/

Chicago Manual of Style (Bibliography):

Haag, Michael, and Justin Romberg. "Existence and Convergence of Fourier Series." Connexions. July 29, 2010. http://cnx.org/content/m10745/2.5/.

Chicago Manual of Style (Note):

Michael Haag and Justin Romberg, "Existence and Convergence of Fourier Series," Connexions, July 29, 2010, http://cnx.org/content/m10745/2.5/.

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

Haag, M., & Romberg, J. 2010. Existence and Convergence of Fourier Series. Connexions, July 29, 2010. http://cnx.org/content/m10745/2.5/.

Modern Languages Association (MLA) Style Manual:

Haag, Michael, and Justin Romberg. Existence and Convergence of Fourier Series. Connexions. 29 July 2010 <http://cnx.org/content/m10745/2.5/>.