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About: Complex Fourier Series

Module by: Don Johnson. E-mail the author

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Name: Complex Fourier Series
ID: m0042
Language: English (en)
Summary: Definition of the complex Fourier series.
Subject: Science and Technology
Keywords: complex Fourier series, conjugate symmetry, Euler relations, Fourier coefficients, Fourier series, orthogonality, Parseval's theorem, periodic signal, power, pulse, spectrum, square wave
License: Creative Commons Attribution License CC-BY 1.0

Authors: Don Johnson (dhj@rice.edu)
Copyright Holders: Don Johnson (dhj@rice.edu)
Maintainers: Don Johnson (dhj@rice.edu), Shawn Stewart (mrshawn@alumni.rice.edu), Benjamin Fite (bfite@rice.edu)

Latest version: 2.29 (history)
First publication date: Jul 24, 2000 12:00 am GMT-5
Last revision to module: Aug 8, 2009 6:45 pm GMT-5

Module XML: m0042_2.29.cnxml

Version History

Version: 2.29 Aug 8, 2009 6:45 pm GMT-5 by Don Johnson
Changes:
Fixed a typo.

Version: 2.28 Jul 6, 2009 5:13 pm GMT-5 by Don Johnson
Changes:
Fixed some math typos.

Version: 2.27 Jun 4, 2009 12:01 pm GMT-5 by Connexions
Changes:
Modified markup for explicit .eps image reference

Version: 2.26 Oct 8, 2008 8:53 am GMT-5 by Don Johnson
Changes:
Fixed a typo and some formatting errors.

Version: 2.25 Oct 6, 2008 9:09 am GMT-5 by Don Johnson
Changes:
Reworded some things.

Version: 2.24 Aug 9, 2008 4:56 pm GMT-5 by Don Johnson
Changes:
Fixed an error in the solution to the first exercise.

Version: 2.23 Aug 4, 2008 5:03 pm GMT-5 by Don Johnson
Changes:
Made module the first one on Fourier series.

Version: 2.22 May 10, 2007 3:56 pm GMT-5 by Don Johnson
Changes:
Fixed some bad paragraph breaks and some bad wording.

Version: 2.21 Apr 13, 2005 9:47 am GMT-5 by Charlet Reedstrom
Changes:
update to cnxml-0.5

Version: 2.20 Oct 2, 2003 8:31 am GMT-5 by Don Johnson
Changes:
Fixed a math error in the first exercise.

Version: 2.19 Aug 18, 2003 11:17 pm GMT-5 by Don Johnson
Changes:
Fixed a link error.

Version: 2.18 Jul 27, 2003 5:02 pm GMT-5 by Don Johnson
Changes:
Corrected link error.

Version: 2.17 Jul 27, 2003 4:55 pm GMT-5 by Don Johnson
Changes:
Fixed intermodule link errors.

Version: 2.16 Sep 30, 2002 12:00 am GMT-5 by (Unknown)
Changes:
Fixed some minor math errors.

Version: 2.15 Aug 23, 2002 12:00 am GMT-5 by (Unknown)
Changes:
- ran spectrum3.eps through eps2eps

Version: 2.14 Aug 16, 2002 12:00 am GMT-5 by (Unknown)
Changes:
Moved a sentence around.

Version: 2.13 Jun 27, 2002 12:00 am GMT-5 by (Unknown)
Changes:
updated module to 4.0 and corrected typos

Version: 2.12 Apr 12, 2002 12:00 am GMT-5 by (Unknown)
Changes:
changed how conditions on equations were marked up - used forall

Version: 2.11 Mar 27, 2002 12:00 am US/Central by (Unknown)
Changes:
edited alot of mathml and some cnxml

Version: 2.10 Oct 4, 2001 12:00 am GMT-5 by (Unknown)
Changes:
Fixed integral problem.

Version: 2.9 Oct 2, 2001 12:00 am GMT-5 by (Unknown)
Changes:
Fixed inline integral error.

Version: 2.8 Oct 2, 2001 12:00 am GMT-5 by (Unknown)
Changes:
Fixed tau errors.

Version: 2.7 Sep 11, 2001 12:00 am GMT-5 by Brent Hendricks
Changes:
Converted to CNXML 0.3.5

Version: 2.6 Aug 24, 2001 12:00 am GMT-5 by (Unknown)
Changes:
Changed keywords.

Version: 2.5 Aug 23, 2001 12:00 am GMT-5 by (Unknown)
Changes:
fixed white space problems

Version: 2.4 Aug 20, 2001 12:00 am GMT-5 by (Unknown)
Changes:
I reuploaded the images and their corresponding .eps files.

Version: 2.3 Jul 17, 2001 12:00 am GMT-5 by (Unknown)
Changes:
Remodularized, some minor fixes.

Version: 2.2 May 30, 2001 12:00 am GMT-5 by (Unknown)
Changes:
Corrected keyword and version number

Version: 2.1 May 29, 2001 12:00 am GMT-5 by (Unknown)
Changes:
Cleaned up MathML and general upgrade to 0.3.

Version: 2.0 Jul 24, 2000 12:00 am GMT-5 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 1.0) of this work:

American Chemical Society (ACS) Style Guide:

Johnson, D. Complex Fourier Series, Connexions Web site. http://cnx.org/content/m0042/2.29/, Aug 8, 2009.

American Medical Assocation (AMA) Manual of Style:

Johnson D. Complex Fourier Series [Connexions Web site]. August 8, 2009. Available at: http://cnx.org/content/m0042/2.29/.

American Psychological Assocation (APA) Publication Manual:

Johnson, D. (2009, August 8). Complex Fourier Series. Retrieved from the Connexions Web site: http://cnx.org/content/m0042/2.29/

Chicago Manual of Style (Bibliography):

Johnson, Don. "Complex Fourier Series." Connexions. August 8, 2009. http://cnx.org/content/m0042/2.29/.

Chicago Manual of Style (Note):

Don Johnson, "Complex Fourier Series," Connexions, August 8, 2009, http://cnx.org/content/m0042/2.29/.

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

Johnson, D. 2009. Complex Fourier Series. Connexions, August 8, 2009. http://cnx.org/content/m0042/2.29/.

Modern Languages Association (MLA) Style Manual:

Johnson, Don. Complex Fourier Series. Connexions. 8 Aug. 2009 <http://cnx.org/content/m0042/2.29/>.