Mathematics Homework Solutions
Problem
#27406

Gibb's Phenomenon (Spurious Oscillations; Truncated Fourier Series; Overshoot; Undershoot)

4. In this problem, you will devise a computer experiment to investigate Gibb's phenomenon, which is the presence of spurious oscillations in the graph of a truncated Fourier series near the places where the full Fourier series is discontinous.

Choose any function you like that demonstrates Gibb's phenomenon. Your goal is to answer these two questions:
(a) You should find that the amount of overshoot only depends on the height of the discontinuity of your function. Expressed as a ratio to the height of the discontinuity, what is the approximate amount of overshoot/undershoot?
(b) What happens to the amount of overshoot/undershoot as you increadse the number of terms in your truncated Fourier series?

*Please see attachment for complete directions

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PLEASE INCLUDE MATHEMATICA CODE.

Solution Summary

The Gibbs phenomenon occurs at points where the derivative of the function is discontinuous.
This assignment demonstrates the Gibbs phenomenon with graphs and numerical analysis.

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