Gibbs Phenomenon
In mathematics, the Gibbs phenomenon, discovered by Henry Wilbraham (1848) and rediscovered by J. Willard Gibbs (1899), is the peculiar manner in which the Fourier series of a piecewise continuously differentiable periodic function behaves at a jump discontinuity: the nth partial sum of the Fourier series has large oscillations near the jump, which might increase the maximum of the partial sum above that of the function itself. The overshoot does not die out as the frequency increases, but approaches a finite limit.
These are one cause of ringing artifacts in signal processing.
Read more about Gibbs Phenomenon: Description, Formal Mathematical Description of The Phenomenon, Signal Processing Explanation, The Square Wave Example, Consequences
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“Since everything in nature answers to a moral power, if any phenomenon remains brute and dark, it is that the corresponding faculty in the observer is not yet active.”
—Ralph Waldo Emerson (1803–1882)