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About: Classic Fourier Series

Module by: Don Johnson. E-mail the author

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Name: Classic Fourier Series
ID: m0039
Language: English (en)
Summary: Signals can be composed by a superposition of an infinite number of sine and cosine functions. The coefficients of the superposition depend on the signal being represented and are equivalent to knowing the function itself.
Subject: Mathematics and Statistics
Keywords: Euler, Fourier coefficients, Fourier series, frequency, Gauss, orthogonality, sinusoid, square wave
License: Creative Commons Attribution License CC-BY 3.0

Authors: Don Johnson (dhj@rice.edu)
Copyright Holders: Don Johnson (dhj@rice.edu)
Maintainers: Don Johnson (dhj@rice.edu), Roy Ha (rha@alumni.rice.edu), Benjamin Fite (bfite@rice.edu)

Latest version: 2.24 (history)
First publication date: Jul 21, 2000 12:00 am -0500
Last revision to module: May 16, 2013 11:01 am -0500

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Version History

Version: 2.24 May 16, 2013 11:01 am -0500 by Don Johnson
Changes:
Fixed a typo.

Version: 2.23 Jul 15, 2010 3:09 pm -0500 by Don Johnson
Changes:
Upgrade.

Version: 2.22 Aug 5, 2008 10:58 am -0500 by Don Johnson
Changes:
Fixed some formatting errors.

Version: 2.21 Aug 4, 2008 5:00 pm -0500 by Don Johnson
Changes:
Rewrote now that module follows the one on complex Fourier series.

Version: 2.20 Apr 18, 2005 3:23 pm -0500 by Charlet Reedstrom
Changes:
update to cnxml-0.5, fix typo, mi to mn where needed

Version: 2.19 Aug 17, 2004 10:07 pm -0500 by Brent Hendricks
Changes:
- Removed Makefile, fixed equation error

Version: 2.18 Jul 14, 2004 5:04 pm -0500 by Don Johnson
Changes:
Fixed error on integral of square of a sinusoid.

Version: 2.17 Oct 2, 2003 4:12 pm -0500 by Don Johnson
Changes:
Fixed a math error.

Version: 2.16 Jul 31, 2003 9:56 pm -0500 by Don Johnson
Changes:
Fixed bounding variable markup error.

Version: 2.15 Aug 8, 2002 12:00 am -0500 by (Unknown)
Changes:
Revised extensively.

Version: 2.14 Jun 26, 2002 12:00 am -0500 by (Unknown)
Changes:
updated module

Version: 2.13 Mar 6, 2002 12:00 am -0600 by (Unknown)
Changes:
edited math - one equation is too long for hardcopy

Version: 2.12 Sep 24, 2001 12:00 am -0500 by (Unknown)
Changes:
Fixed typo before eq. 109 and a typo in eq. 113.

Version: 2.11 Sep 11, 2001 12:00 am -0500 by Brent Hendricks
Changes:
Converted to CNXML 0.3.5

Version: 2.10 Aug 24, 2001 12:00 am -0500 by (Unknown)
Changes:
- fix subscripts

Version: 2.9 Aug 24, 2001 12:00 am -0500 by (Unknown)
Changes:
Changed <m:and/> to <m:mo>and</m:mo> (Jenn).

Version: 2.8 Aug 24, 2001 12:00 am -0500 by (Unknown)
Changes:
Changed keywords.

Version: 2.7 Aug 23, 2001 12:00 am -0500 by (Unknown)
Changes:
fixed punctuation whitespace errors

Version: 2.6 Aug 20, 2001 12:00 am -0500 by (Unknown)
Changes:
I re-uploaded the image files and their corresponding eps files.

Version: 2.5 Aug 15, 2001 12:00 am -0500 by (Unknown)
Changes:
- Change m:pi to &pi;
- Surround pi with m:cn

Version: 2.4 Aug 15, 2001 12:00 am -0500 by (Unknown)
Changes:
- Fixed some s/mi/ci problems

Version: 2.3 Jul 17, 2001 12:00 am -0500 by (Unknown)
Changes:
Remodularized, some minor fixes.

Version: 2.2 May 30, 2001 12:00 am -0500 by (Unknown)
Changes:
Updated abstract and put multi-word keywords in correct order

Version: 2.1 May 24, 2001 12:00 am -0500 by (Unknown)
Changes:
Updated module to cnxml ver. 0.3

Version: 2.0 Aug 9, 2000 12:00 am -0500 by Brent Hendricks
Changes:
Bumped version to 2.0

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The following citation styles comply with the attribution requirements for the license (CC-BY 3.0) of this work:

American Chemical Society (ACS) Style Guide:

Johnson, D. Classic Fourier Series, Connexions Web site. http://cnx.org/content/m0039/2.24/, May 16, 2013.

American Medical Assocation (AMA) Manual of Style:

Johnson D. Classic Fourier Series [Connexions Web site]. May 16, 2013. Available at: http://cnx.org/content/m0039/2.24/.

American Psychological Assocation (APA) Publication Manual:

Johnson, D. (2013, May 16). Classic Fourier Series. Retrieved from the Connexions Web site: http://cnx.org/content/m0039/2.24/

Chicago Manual of Style (Bibliography):

Johnson, Don. "Classic Fourier Series." Connexions. May 16, 2013. http://cnx.org/content/m0039/2.24/.

Chicago Manual of Style (Note):

Don Johnson, "Classic Fourier Series," Connexions, May 16, 2013, http://cnx.org/content/m0039/2.24/.

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

Johnson, D. 2013. Classic Fourier Series. Connexions, May 16, 2013. http://cnx.org/content/m0039/2.24/.

Modern Languages Association (MLA) Style Manual:

Johnson, Don. Classic Fourier Series. Connexions. 16 May 2013 <http://cnx.org/content/m0039/2.24/>.