Gibbs Phenomenon

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>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.

Showing the spike at a discontinuity.

References

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Contributor

• Joshua Grant