Gibbs Phenomenon

[watersprite]

Please can or will someone explain in easy terms The Gibbs Phenomenon and the Fourier Sequence?

thanks,
~ k

 

[tree]

https://en.wikipedia.org/wiki/Gibbs_phenomenon
https://en.wikipedia.org/wiki/Fourier_series
http://mathworld.wolfram.com/GibbsPhenomenon.html
http://www.gaussianwaves.com/2010/04/gibbs-phenomena-a-demonstration/

Indeed, that would be something to see explained so
that I could understand it. There are a number of
lectures/explanations on youtube.

 

[tree]

Please can or will someone explain in easy terms The Gibbs Phenomenon and the Fourier Sequence?

thanks,
~ k

Post #2 in no way implies
that I have the slightest
idea what this is about.

 

[apt-get]

A Fourier series is a way to write a function as an infinite sum of sine and cosine functions. Of course, when dealing with that, one can only ever actually write down an approximation. The Gibbs phenomena happens when one tries to approximate discontinuous functions with as a finite sum of continuous functions (ie, sines and cosines). In the case of approximating a square wave, it happens near where all of the sine terms in the series are zero, but are non-zero nearby, since this is approximating the discontinuity. Discontinuities in math are where things happen and adding many terms together results in areas nearby that zero crossing that don't perfectly cancel each other out and you get the Gibbs phenomena.

 

[StephF]

I thought the Gibbs phenomenon was when Mark Harmon slapped someone on the back of the head.

 

[Warmheart]

 

[tree]

This was a Gibbs Phenomenon, for awhile.
https://en.wikipedia.org/wiki/Bee_Gees