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Complex Fourier Series
| Name: | Complex Fourier Series |
| ID: | m0042 |
| Language: | English (en) |
| Summary: | |
| 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 3.0 |
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| 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) |
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| Latest version: | 2.31 (history) |
| First publication date: | Jul 24, 2000 12:00 am -0500 |
| Last revision to module: | Sep 21, 2011 8:52 am -0500 |
| PDF: | m0042_2.31.pdf | PDF file, for viewing content offline and printing. Learn more. |
| EPUB: | m0042_2.31.epub | Electronic publication file, for viewing in handheld devices. Learn more. |
| XML: | m0042_2.31.cnxml | XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more. |
| Source Export ZIP: | m0042_2.31.zip | ZIP containing the module XML plus any included media files. Can be reimported in the editing interface. Learn more. |
| Offline ZIP: | m0042_2.31_offline.zip | An offline HTML copy of the content. Also includes XML, included media files, and other support files. Learn more. |
| Version: | 2.32 May 16, 2013 10:58 am -0500 by Don Johnson |
| Changes: | Fixed a typo. |
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| Version: | 2.31 Sep 21, 2011 8:52 am -0500 by Don Johnson Currently viewing this version. |
| Changes: | Fixed an inequality typo. |
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| Version: | 2.30 Nov 18, 2010 6:40 pm -0600 by Don Johnson |
| Changes: | Fixed minor typos. |
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| Version: | 2.29 Aug 8, 2009 6:45 pm -0500 by Don Johnson |
| Changes: | Fixed a typo. |
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| Version: | 2.28 Jul 6, 2009 5:13 pm -0500 by Don Johnson |
| Changes: | Fixed some math typos. |
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| Version: | 2.27 Jun 4, 2009 12:01 pm -0500 by Connexions |
| Changes: | Modified markup for explicit .eps image reference |
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| Version: | 2.26 Oct 8, 2008 8:53 am -0500 by Don Johnson |
| Changes: | Fixed a typo and some formatting errors. |
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| Version: | 2.25 Oct 6, 2008 9:09 am -0500 by Don Johnson |
| Changes: | Reworded some things. |
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| Version: | 2.24 Aug 9, 2008 4:56 pm -0500 by Don Johnson |
| Changes: | Fixed an error in the solution to the first exercise. |
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| Version: | 2.23 Aug 4, 2008 5:03 pm -0500 by Don Johnson |
| Changes: | Made module the first one on Fourier series. |
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| Version: | 2.22 May 10, 2007 3:56 pm -0500 by Don Johnson |
| Changes: | Fixed some bad paragraph breaks and some bad wording. |
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| Version: | 2.21 Apr 13, 2005 9:47 am -0500 by Charlet Reedstrom |
| Changes: | update to cnxml-0.5 |
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| Version: | 2.20 Oct 2, 2003 8:31 am -0500 by Don Johnson |
| Changes: | Fixed a math error in the first exercise. |
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| Version: | 2.19 Aug 18, 2003 11:17 pm -0500 by Don Johnson |
| Changes: | Fixed a link error. |
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| Version: | 2.18 Jul 27, 2003 5:02 pm -0500 by Don Johnson |
| Changes: | Corrected link error. |
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| Version: | 2.17 Jul 27, 2003 4:55 pm -0500 by Don Johnson |
| Changes: | Fixed intermodule link errors. |
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| Version: | 2.16 Sep 30, 2002 12:00 am -0500 by (Unknown) |
| Changes: | Fixed some minor math errors. |
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| Version: | 2.15 Aug 23, 2002 12:00 am -0500 by (Unknown) |
| Changes: | - ran spectrum3.eps through eps2eps |
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| Version: | 2.14 Aug 16, 2002 12:00 am -0500 by (Unknown) |
| Changes: | Moved a sentence around. |
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| Version: | 2.13 Jun 27, 2002 12:00 am -0500 by (Unknown) |
| Changes: | updated module to 4.0 and corrected typos |
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| Version: | 2.12 Apr 12, 2002 12:00 am -0500 by (Unknown) |
| Changes: | changed how conditions on equations were marked up - used forall |
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| Version: | 2.11 Mar 27, 2002 12:00 am -0600 by (Unknown) |
| Changes: | edited alot of mathml and some cnxml |
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| Version: | 2.10 Oct 4, 2001 12:00 am -0500 by (Unknown) |
| Changes: | Fixed integral problem. |
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| Version: | 2.9 Oct 2, 2001 12:00 am -0500 by (Unknown) |
| Changes: | Fixed inline integral error. |
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| Version: | 2.8 Oct 2, 2001 12:00 am -0500 by (Unknown) |
| Changes: | Fixed tau errors. |
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| Version: | 2.7 Sep 11, 2001 12:00 am -0500 by Brent Hendricks |
| Changes: | Converted to CNXML 0.3.5 |
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| Version: | 2.6 Aug 24, 2001 12:00 am -0500 by (Unknown) |
| Changes: | Changed keywords. |
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| Version: | 2.5 Aug 23, 2001 12:00 am -0500 by (Unknown) |
| Changes: | fixed white space problems |
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| Version: | 2.4 Aug 20, 2001 12:00 am -0500 by (Unknown) |
| Changes: | I reuploaded the images and their corresponding .eps files. |
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| Version: | 2.3 Jul 17, 2001 12:00 am -0500 by (Unknown) |
| Changes: | Remodularized, some minor fixes. |
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| Version: | 2.2 May 30, 2001 12:00 am -0500 by (Unknown) |
| Changes: | Corrected keyword and version number |
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| Version: | 2.1 May 29, 2001 12:00 am -0500 by (Unknown) |
| Changes: | Cleaned up MathML and general upgrade to 0.3. |
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| Version: | 2.0 Jul 24, 2000 12:00 am -0500 by Brent Hendricks |
| Changes: | Bumped version to 2.0 |
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If you reuse this work elsewhere, in order to comply with the attribution requirements of the license (CC-BY 3.0), you must include
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The following citation styles comply with the attribution requirements for the license (CC-BY 3.0) of this work:
Johnson, D. Complex Fourier Series, Connexions Web site. http://cnx.org/content/m0042/2.31/, Sep 21, 2011.
Johnson D. Complex Fourier Series [Connexions Web site]. September 21, 2011. Available at: http://cnx.org/content/m0042/2.31/.
Johnson, D. (2011, September 21). Complex Fourier Series. Retrieved from the Connexions Web site: http://cnx.org/content/m0042/2.31/
Johnson, Don. "Complex Fourier Series." Connexions. September 21, 2011. http://cnx.org/content/m0042/2.31/.
Don Johnson, "Complex Fourier Series," Connexions, September 21, 2011, http://cnx.org/content/m0042/2.31/.
Johnson, D. 2011. Complex Fourier Series. Connexions, September 21, 2011. http://cnx.org/content/m0042/2.31/.
Johnson, Don. Complex Fourier Series. Connexions. 21 Sep. 2011 <http://cnx.org/content/m0042/2.31/>.
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This work is licensed by Don Johnson under a Creative Commons Attribution License (CC-BY 3.0), and is an Open Educational Resource.
Last edited by Don Johnson on Sep 21, 2011 8:52 am -0500.
