Connexions

Sections
You are here: Home » Content » Complex Fourier Series and Their Properties

About: Complex Fourier Series and Their Properties

Module by: Don Johnson

View content

Metadata

Name: Complex Fourier Series and Their Properties
ID: m0065
Language: English (en)
Summary: This module shows how to find a signal's complex Fourier spectrum. It also lists several properties for that spectrum, including that it obeys Parseval's theorem.
Subject: Mathematics and Statistics, Science and Technology
Keywords: coefficients, Complex, conjugate, Fourier, orthogonality, Parseval, Parseval's, power, series, spectral, spectrum, square, symmetry, wave
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
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), Doug Daniels (ddaniels888@gmail.com)
Version: 2.7 (history)
Created: Aug 11, 2000 12:00 am GMT-5
Revised: Aug 4, 2004 3:44 pm GMT-5

Version History

Version: 2.7 Aug 4, 2004 3:44 pm GMT-5 by Elizabeth Gregory
Changes: 
Updated to CNXML 0.5
Version: 2.6 Apr 15, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
resubmit because somehow my changes did not get uploaded into the system on Friday
Version: 2.5 Apr 12, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
edited math such as power marked as superscript, conjugate marked as superscript etc
Version: 2.4 Sep 11, 2001 12:00 am GMT-5 by Brent Hendricks
Changes: 
Converted to CNXML 0.3.5
Version: 2.3 Jun 21, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
removed some paragraphs from rules, changed some text to examples
Version: 2.2 May 30, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
none
Version: 2.1 May 29, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
I ported the CNXML 0.1 to 0.3, and rewrote the Presentation MathML in Content MathML.  I also changed the list at the end of the module to a sequence of rule tags.  Additionally, I added keywords and an abstract.
Version: 2.0 Oct 5, 2000 12:00 am GMT-5 by Brent Hendricks
Changes: 
Bumped version to 2.0

How to Reuse and Attribute This Content

If you derive a copy of this content using a Connexions account and publish your version, proper attribution of the original work will be automatically done for you.

If you reuse this work elsewhere, in order to comply with the attribution requirements of the license (CC-BY 1.0), you must include

  • the authors' names: Don Johnson
  • the title of the work: Complex Fourier Series and Their Properties
  • the Connexions URL where the work can be found: http://cnx.org/content/m0065/2.7/

See the citation section below for examples you can copy.

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:

Johnson, D. Complex Fourier Series and Their Properties, Connexions Web site. http://cnx.org/content/m0065/2.7/, Aug 4, 2004.

American Medical Assocation (AMA) Manual of Style:

Johnson D. Complex Fourier Series and Their Properties [Connexions Web site]. August 4, 2004. Available at: http://cnx.org/content/m0065/2.7/.

American Psychological Assocation (APA) Publication Manual:

Johnson, D. (2004, August 4). Complex Fourier Series and Their Properties. Retrieved from the Connexions Web site: http://cnx.org/content/m0065/2.7/

Chicago Manual of Style (Bibliography):

Johnson, Don. "Complex Fourier Series and Their Properties." Connexions. August 4, 2004. http://cnx.org/content/m0065/2.7/.

Chicago Manual of Style (Note):

Don Johnson, "Complex Fourier Series and Their Properties," Connexions, August 4, 2004, http://cnx.org/content/m0065/2.7/.

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

Johnson, D. 2004. Complex Fourier Series and Their Properties. Connexions, August 4, 2004. http://cnx.org/content/m0065/2.7/.

Modern Languages Association (MLA) Style Manual:

Johnson, Don. Complex Fourier Series and Their Properties. Connexions. 4 Aug. 2004 <http://cnx.org/content/m0065/2.7/>.