gibbs phenomenon
Word Rarity
Rare
Frequency: Zipf frequency 3.53 in modern English
27
Scrabble Score
15
Letters
3
Syllables
10
Unique Chars
Meaning
name
A behaviour of the Fourier series approximation at a jump discontinuity of a piecewise continuously differentiable periodic function, such that partial sums exhibit an oscillation peak adjacent the discontinuity that may overshoot the function maximum (or minimum) itself and does not disappear as more terms are calculated, but rather approaches a finite limit.
Example Sentences
- "The Gibbs phenomenon is characteristic of Fourier series at a discontinuity, its size being proportional to the magnitude of the discontinuity."
- "At a point of discontinuity, the oscillations accompanying the Gibbs phenomenon have an overshoot of approximately 18% of the amplitude of the discontinuity."
- "The observed “ringing” is due to the Gibbs phenomenon, which relates to the inability of a finite Fourier spectrum to reproduce sharp edges."
Etymology
After J. Willard Gibbs, who identified the behaviour in 1899, unaware of its previous discovery in 1848 by Henry Wilbraham. A widespread myth has it that the phenomenon was observed in a device developed in 1898 by Albert A. Michelson to compute and synthesise Fourier series, but that it was assumed due to physical imperfections in the device. In fact, the graphs produced were not precise enough for the phenomenon to be clearly observed, and Michelson made no mention of it in a paper describing the device.
Inflected Forms
Gibbs' (alternative)
phenomenon (alternative)