Meaning of Gibbs phenomenon | Babel Free

Definitions

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.

Examples

“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.”

CEFR level