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Gibbs phenomenon

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Creator
Seonglae ChoSeonglae Cho
Created
Created
2023 Oct 7 5:24
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Seonglae ChoSeonglae Cho
Edited
Edited
2023 Oct 7 5:25
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Converge almost everywhere except points of discontinuity when approximate

 
 
 
 
 
 
Gibbs phenomenon
In mathematics, the Gibbs phenomenon is the oscillatory behavior of the Fourier series of a piecewise continuously differentiable periodic function around a jump discontinuity. The N {\textstyle N} th partial Fourier series of the function (formed by summing the N {\textstyle N} lowest constituent sinusoids of the Fourier series of the function) produces large peaks around the jump which overshoot and undershoot the function values. As more sinusoids are used, this approximation error approaches a limit of about 9% of the jump, though the infinite Fourier series sum does eventually converge almost everywhere (pointwise convergence on continuous points) except points of discontinuity.[1]
Gibbs phenomenon
https://en.wikipedia.org/wiki/Gibbs_phenomenon
 
 

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Gibbs phenomenon
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