| 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 |
| Document Type: | -//CNX//DTD CNXML 0.5 plus MathML//EN |
| License: | Creative Commons Attribution License (CC-BY 1.0) |
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| 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) |
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| Version: | 2.22 (history) |
| Created: | Jul 21, 2000 12:00 am GMT-5 |
| Revised: | Aug 5, 2008 10:58 am GMT-5 |
| Version: | 2.22 Aug 5, 2008 10:58 am GMT-5 by Don Johnson |
| Changes: | Fixed some formatting errors. |
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| Version: | 2.21 Aug 4, 2008 5:00 pm GMT-5 by Don Johnson |
| Changes: | Rewrote now that module follows the one on complex Fourier series. |
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| Version: | 2.20 Apr 18, 2005 3:23 pm GMT-5 by Charlet Reedstrom |
| Changes: | update to cnxml-0.5, fix typo, mi to mn where needed |
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| Version: | 2.19 Aug 17, 2004 10:07 pm GMT-5 by Brent Hendricks |
| Changes: | - Removed Makefile, fixed equation error |
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| Version: | 2.18 Jul 14, 2004 5:04 pm GMT-5 by Don Johnson |
| Changes: | Fixed error on integral of square of a sinusoid. |
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| Version: | 2.17 Oct 2, 2003 4:12 pm GMT-5 by Don Johnson |
| Changes: | Fixed a math error. |
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| Version: | 2.16 Jul 31, 2003 9:56 pm GMT-5 by Don Johnson |
| Changes: | Fixed bounding variable markup error. |
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| Version: | 2.15 Aug 8, 2002 12:00 am GMT-5 by (Unknown) |
| Changes: | Revised extensively. |
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| Version: | 2.14 Jun 26, 2002 12:00 am GMT-5 by (Unknown) |
| Changes: | updated module |
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| Version: | 2.13 Mar 6, 2002 12:00 am US/Central by (Unknown) |
| Changes: | edited math - one equation is too long for hardcopy |
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| Version: | 2.12 Sep 24, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | Fixed typo before eq. 109 and a typo in eq. 113. |
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| Version: | 2.11 Sep 11, 2001 12:00 am GMT-5 by Brent Hendricks |
| Changes: | Converted to CNXML 0.3.5 |
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| Version: | 2.10 Aug 24, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | - fix subscripts |
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| Version: | 2.9 Aug 24, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | Changed <m:and/> to <m:mo>and</m:mo> (Jenn). |
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| Version: | 2.8 Aug 24, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | Changed keywords. |
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| Version: | 2.7 Aug 23, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | fixed punctuation whitespace errors |
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| Version: | 2.6 Aug 20, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | I re-uploaded the image files and their corresponding eps files. |
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| Version: | 2.5 Aug 15, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | - Change m:pi to π - Surround pi with m:cn |
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| Version: | 2.4 Aug 15, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | - Fixed some s/mi/ci problems |
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| Version: | 2.3 Jul 17, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | Remodularized, some minor fixes. |
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| Version: | 2.2 May 30, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | Updated abstract and put multi-word keywords in correct order |
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| Version: | 2.1 May 24, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | Updated module to cnxml ver. 0.3 |
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| Version: | 2.0 Aug 9, 2000 12:00 am GMT-5 by Brent Hendricks |
| Changes: | Bumped version to 2.0 |
If you reuse this work, in order to comply with the attribution requirements of the license (CC-BY 1.0), you must include the
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.
The following citation styles comply with the attribution requirements for the license (CC-BY 1.0) of this work:
Johnson, D. Classic Fourier Series, Connexions Web site. http://cnx.org/content/m0039/2.22/, Aug 5, 2008.
Johnson D. Classic Fourier Series [Connexions Web site]. August 5, 2008. Available at: http://cnx.org/content/m0039/2.22/.
Johnson, D. (2008, August 5). Classic Fourier Series. Retrieved from the Connexions Web site: http://cnx.org/content/m0039/2.22/
Johnson, Don. "Classic Fourier Series." Connexions. August 5, 2008. http://cnx.org/content/m0039/2.22/.
Don Johnson, "Classic Fourier Series," Connexions, August 5, 2008, http://cnx.org/content/m0039/2.22/.
Johnson, D. 2008. Classic Fourier Series. Connexions, August 5, 2008. http://cnx.org/content/m0039/2.22/.
Johnson, Don. Classic Fourier Series. Connexions. 5 Aug. 2008 <http://cnx.org/content/m0039/2.22/>.