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Gibbs Phenomenon and Fourier Series expansion

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?

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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.