Gibbs phenomenon
Gibbs phenomenon proper noun: 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.
Proper noun
Gibbs phenomenon
- 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.
- The Gibbs phenomenon is characteristic of Fourier series at a discontinuity, its size being proportional to the magnitude of the discontinuity.1974, K. F. Riley, Mathematical Methods for the Physical Sciences, Cambridge University Press, page 197
- At a point of discontinuity, the oscillations accompanying the Gibbs phenomenon have an overshoot of approximately 18% of the amplitude of the discontinuity.1999, Werner S. Weiglhofer, Kenneth A. Lindsay, Ordinary Differential Equations and Applications, page 121
Gibbs phenomenon meaning in Tamil
Gibbs phenomenon in Tamil
- கிப்பினதுதோற்றப்பாடு
Forms of Gibbs phenomenon
| alternative form | Gibbs' |
|---|---|
| alternative form | phenomenon |
Origin of Gibbs phenomenon
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.
Questions about Gibbs phenomenon
- What does Gibbs phenomenon mean?
- Gibbs phenomenon means 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.
- What is Gibbs phenomenon in Tamil?
- Gibbs phenomenon in Tamil is கிப்பினதுதோற்றப்பாடு. See Gibbs phenomenon meaning in Tamil.
- What part of speech is Gibbs phenomenon?
- Gibbs phenomenon is a proper noun.
Words near Gibbs phenomenon in the dictionary
Source and license
Adapted from Wiktionary: Gibbs phenomenon (page history and authors); gibbs phenomenon (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Cite this entry: “Gibbs phenomenon.” Word.ws, https://word.ws/gibbs_phenomenon. Based on Wiktionary, CC BY-SA 4.0.