Class Wiki - User contributions [en]

Fourier Series: Explained!

2010-01-12T16:42:46Z

Jgrant:

==A Brief Introduction==
A Fourier series is a mathematical tool that takes a periodic function and turns it into a sum of simple oscillating functions (i.e. sines and cosines)<ref> [http://en.wikipedia.org/wiki/Fourier_series Fourier Series]</ref>. These series were discovered by Joseph Fourier to solve a heat equation in a metal plate.

==How They Work==
A Fourier Series represents a periodic function through a sum of sines or cosines. Each term in the summation has a frequency n. The first term has the same frequency as the periodic function, the second term has twice the frequency of the periodic function, and so on. The more functions added, the more the summation resembles the step function. Observe the animation; notice how the summation function resembles the original periodic function more as more functions are added.
[[Image:Square Wave.jpg|500px|thumb|right|Square Wave with similar periods to the cosine function]]
[[Image:Fourier Animated.gif|500px|thumb|left|Fourier series animated to show increasing accuracy as evaluation bounds are increased.]]
==References==
<references/>
==Helpful Links==
[http://www.fourier-series.com/fourierseries2/flash_programs/fourier_series_sin_cos/index.html A very helpful game]
==Contributors==
*[[Lau, Chris | Christopher Garrison Lau I]]
*[[Vier, Michael|Michael Vier]]
==Reviewed By==
*[[Grant, Joshua|Joshua Grant]]

Fourier Series: Explained!

2010-01-12T16:42:28Z

Jgrant:

Fourier Series: Explained!

2010-01-12T16:41:50Z

Jgrant:

Winter 2010

2010-01-12T16:36:55Z

Jgrant:

Put links for your reports here. Someone feel free to edit this better.

Links to the posted reports are found under the publishing author's name. (Like it says above, if you hate it...change it! I promise I won’t cry. Brandon)

1. [[Biesenthal, Dan]]

2. [[Blackley, Ben]]

3. [[Cruz, Jorge]]

4. [[Fullerton, Colby]]
<math>\Rightarrow</math> [[Laplace Transform]]

5. [[Grant, Joshua]]

6. [[Gratias, Ryan]]

7. [[Hawkins, John]]

<math>\Rightarrow</math> [[Excercise: Sawtooth Wave Fourier Transform]]

8. [[Lau, Chris]]

9. [[Roath, Brian]]
<math>\Rightarrow</math> [[Laplace Transform]]

10. [[Robbins, David]]

11. [[Roth, Andrew]]
<math>\Rightarrow</math> [[Example: LaTex format (0 points)]]
<math>\Rightarrow</math> [[Chapter 22--Fourier Series: Fundamental Period, Frequency, and Angular Frequency]]

12. [[Vazquez, Brandon]]

13. [[Vier, Michael]]

14. [[Wooley, Thomas]]

15. [[Jaymin, Joseph]]

==Draft Articles==
These articles are not ready for reading and error checking. They are listed so people will not simultaneously write about similar topics.
* [[Fourier Series: Explained!]]
* [[Gibbs Phenomenon]]

Gibbs Phenomenon

2010-01-12T16:34:45Z

Jgrant:

==Overview==
The Gibbs phenomenon is the the tendency for Fourier sums to "jump" higher than expected at discontinuities. It is named after the American physicist J. Willard Gibbs.

==The Phenomenon==
The identifying characteristic of the Gibbs phenomenon is the spike past where the Fourier series is summing to. As my colleagues previously stated, "notice how the summation function resembles the original periodic function more as more functions are added."<ref>[http://fweb/class-wiki/index.php/Fourier_Series:_Explained! Fourier Series: Explained!]</ref>
While this is true, it can also be seen that the jump does not diminish as the frequency of additional functions is increased. In fact the spike reaches a finite limit.
[[Image:Gibbs_phenomenon_50.jpg|300px|thumb|right|Showing the spike at a discontinuity.]]

==References==
<references/>

==Contributor==
*[[Grant, Joshua | Joshua Grant]]

===Reviewed By===

===Read By===

Gibbs Phenomenon

2010-01-12T16:34:11Z

Jgrant:

==Overview==
The Gibbs phenomenon is the the tendency for Fourier sums to "jump" higher than expected at discontinuities. It is named after the American physicist J. Willard Gibbs.

==The Phenomenon==
The identifying characteristic of the Gibbs phenomenon is the spike past where the Fourier series is summing to. As my colleagues previously stated, "notice how the summation function resembles the original periodic function more as more functions are added."<ref>[http://fweb/class-wiki/index.php/Fourier_Series:_Explained! Fourier Series: Explained!]</ref>
While this is true, it can also be seen that the jump does not diminish as the frequency of additional functions is increased. In fact the spike reaches a finite limit.
[[Image:Gibbs_phenomenon_50.jpg|300px|thumb|right|Showing the spike at a discontinuity.]]

==References==
<references/>

===Contributor===
*[[Grant, Joshua | Joshua Grant]]

==Reviewed By==

===Read By===

Grant, Joshua

2010-01-12T16:31:51Z

Jgrant: New page: ===Contact Info=== * joshua.grant@wallawalla.edu ===Linear Network Analysis=== In Draft: Gibbs Phenomenon

===Contact Info===
* joshua.grant@wallawalla.edu

===Linear Network Analysis===
In Draft: [[Gibbs Phenomenon]]

Gibbs Phenomenon

2010-01-12T16:27:37Z

Jgrant:

Gibbs Phenomenon

2010-01-12T16:23:35Z

Jgrant:

==Overview==
The Gibbs phenomenon is the the tendency for Fourier sums to "jump" higher than expected at discontinuities. It is named after the American physicist J. Willard Gibbs.

==The Phenomenon==
The identifying characteristic of the Gibbs phenomenon is the spike past where the Fourier series is summing to. As my colleagues previously stated, "notice how the summation function resembles the original periodic function more as more functions are added."<ref>[http://fweb/class-wiki/index.php/Fourier_Series:_Explained! Fourier Series: Explained!]</ref>
While this is true, it can also be seen that the jump does not diminish as the frequency of additional functions is increased.
[[Image:Gibbs_phenomenon_50.jpg|300px|thumb|right|Showing the spike at a discontinuity.]]

==References==
<references/>

==Contributor==
*[[Grant, Joshua | Joshua Grant]]

Gibbs Phenomenon

2010-01-12T15:52:27Z

Jgrant:

==Overview==
The Gibbs phenomenon is the the tendency for Fourier sums to "jump" higher than expected at discontinuities. It is named after the American physicist J. Willard Gibbs.

==The Phenomenon==
The identifying characteristic of the Gibbs phenomenon is the spike past where the Fourier series is summing to. As my colleagues previously stated, "notice how the summation function resembles the original periodic function more as more functions are added."<ref>[http://fweb/class-wiki/index.php/Fourier_Series:_Explained! Fourier Series: Explained!]</ref>
While this is true, it can also be seen that the jump does not diminish as the frequency of additional functions is increased.
[[Image:Gibbs_phenomenon_50.jpg|300px|thumb|right|Showing the spike at a discontinuity.]]

Gibbs Phenomenon

2010-01-12T15:50:59Z

Jgrant:

==Overview==
The Gibbs phenomenon is the the tendency for Fourier sums to "jump" higher than expected at discontinuities. It is named after the American physicist J. Willard Gibbs.

==The Phenomenon==
The identifying characteristic of the Gibbs phenomenon is the spike past where the Fourier series is summing to. As my colleagues previously stated, "notice how the summation function resembles the original periodic function more as more functions are added."<ref>[http://fweb/class-wiki/index.php/Fourier_Series:_Explained! Fourier Series: Explained!]</ref>
While this is true, it can also be seen that the jump does not diminish as the frequency of additional functions is increased.
[[Image:Gibbs_phenomenon_50.jpg|500px|thumb|right|Showing the spike at a discontinuity.]]

File:Gibbs phenomenon 50.jpg

2010-01-12T15:46:35Z

Jgrant: Gibbs phenomenon

Gibbs phenomenon

Gibbs Phenomenon

2010-01-12T15:45:50Z

Jgrant:

Gibbs Phenomenon

2010-01-12T15:34:59Z

Jgrant:

Gibbs Phenomenon

2010-01-12T14:42:56Z

Jgrant: New page: ==Overview== The Gibbs phenomenon is the the tendency for Fourier sums to "jump" higher than expected at discontinuities. It is named after the American physicist J. Willard Gibbs.

==Overview==
The Gibbs phenomenon is the the tendency for Fourier sums to "jump" higher than expected at discontinuities. It is named after the American physicist J. Willard Gibbs.