About: Gibbs's Phenomena
Metadata
| Name: | Gibbs's Phenomena |
| ID: | m10092 |
| Language: | English (en) |
| Summary: | The Fourier Series is the representation of continuous-time, periodic signals in terms of complex exponentials. The Dirichlet conditions suggest that discontinuous signals may have a Fourier Series representation so long as there are a finite number of discontinuities. This seems counter-intuitive, however, as complex exponentials are continuous functions. It does not seem possible to exactly reconstruct a discontinuous function from a set of continuous ones. In fact, it is not. However, it can be if we relax the condition of exactly and replace it with the idea of almost everywhere. This is to say that the reconstruction is exactly the same as the original signal except at a finite number of points. These points, not necessarily suprisingly, occur at the points of discontinuities. |
| Subject: | Science and Technology |
| Keywords: | almost everywhere, fourier series, gibbs phenomenon, nonuniform convergence |
| Document Type: | -//CNX//DTD CNXML 0.5 plus MathML//EN |
| License: | Creative Commons Attribution License (CC-BY 1.0) |
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| Authors: | Ricardo Radaelli-Sanchez (ricky@alumni.rice.edu), Richard Baraniuk (richb@rice.edu) |
| Copyright Holders: | Ricardo Radaelli-Sanchez (ricky@alumni.rice.edu), Richard Baraniuk (richb@rice.edu) |
| Maintainers: | Mariyah Poonawala (mariyah@rice.edu), Prashant Singh (prash@ece.rice.edu), Ricardo Radaelli-Sanchez (ricky@alumni.rice.edu), Justin Romberg (jrom@ece.gatech.edu), Melissa Selik (mselik@alumni.rice.edu), Matthew Hutchinson (mhutch@rice.edu) |
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| Version: | 2.9 (history) |
| Created: | Jun 13, 2001 12:00 am GMT-5 |
| Revised: | Jul 19, 2006 4:37 pm GMT-5 |
Version History
| Version: | 2.9 Jul 19, 2006 4:37 pm GMT-5 by Charlet Reedstrom |
| Changes: | Added Matthew Hutchinson as a Maintainer |
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| Version: | 2.8 Jun 14, 2005 4:09 pm GMT-5 by Charlet Reedstrom |
| Changes: | update to cnxml-0.5, fix typos |
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| Version: | 2.7 Jul 9, 2003 2:05 pm GMT-5 by Charlet Reedstrom |
| Changes: | addmaintainers |
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| Version: | 2.6 Jul 22, 2002 12:00 am GMT-5 by (Unknown) |
| Changes: | Edited links. Added new History section. Corrected typos. |
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| Version: | 2.5 May 29, 2002 12:00 am GMT-5 by (Unknown) |
| Changes: | Audited: Revamped module by editing layout and adding a lot more material. More comphensive explanation of the topic now. Printing checks out. |
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| Version: | 2.4 Nov 20, 2001 12:00 am US/Central by Brent Hendricks |
| Changes: | Updated to CNXML 0.3.5 |
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| Version: | 2.3 Jul 20, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | Added jrom and mselik as maintainers in database |
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| Version: | 2.2 Jun 21, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | Fixed spelling error in name |
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| Version: | 2.1 Jun 13, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | added new module |
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| Version: | 2.0 Jun 13, 2001 12:00 am GMT-5 by (Unknown) |
| Changes: | Added initial template for new module m10092 |
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American Chemical Society (ACS) Style Guide:
Radaelli-Sanchez, R.; Baraniuk, R. Gibbs's Phenomena, Connexions Web site. http://cnx.org/content/m10092/2.9/, Jul 19, 2006.
American Medical Assocation (AMA) Manual of Style:
Radaelli-Sanchez R, Baraniuk R. Gibbs's Phenomena [Connexions Web site]. July 19, 2006. Available at: http://cnx.org/content/m10092/2.9/.
American Psychological Assocation (APA) Publication Manual:
Radaelli-Sanchez, R., & Baraniuk, R. (2006, July 19). Gibbs's Phenomena. Retrieved from the Connexions Web site: http://cnx.org/content/m10092/2.9/
Chicago Manual of Style (Bibliography):
Radaelli-Sanchez, Ricardo, and Richard Baraniuk. "Gibbs's Phenomena." Connexions. July 19, 2006. http://cnx.org/content/m10092/2.9/.
Chicago Manual of Style (Note):
Ricardo Radaelli-Sanchez and Richard Baraniuk, "Gibbs's Phenomena," Connexions, July 19, 2006, http://cnx.org/content/m10092/2.9/.
Chicago Manual of Style (Reference, in Author-Date style):
Radaelli-Sanchez, R., & Baraniuk, R. 2006. Gibbs's Phenomena. Connexions, July 19, 2006. http://cnx.org/content/m10092/2.9/.
Modern Languages Association (MLA) Style Manual:
Radaelli-Sanchez, Ricardo, and Richard Baraniuk. Gibbs's Phenomena. Connexions. 19 July 2006 <http://cnx.org/content/m10092/2.9/>.
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This work is licensed by Ricardo Radaelli-Sanchez and Richard Baraniuk under a Creative Commons Attribution License (CC-BY 1.0).
Last edited by Charlet Reedstrom on Jul 19, 2006 4:37 pm GMT-5.