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Definition of "Gibbs phenomenon" |
the rippling phenomenon in the reconstruction of a function around a discontinuity based on the Fourier series of the function. Specifically, given a discontinuous periodic function ƒ which is square-integrable on its period, the Fourier series of ƒ converges to ƒ in the square mean sense. When the periodic function corresponding to the n first terms of that Fourier series is built, then ripples appear at the vicinity of each discontinuity of ƒ . When n tends to infinity, these ripples tend to zero in the square mean sense, but their maximum amplitude does not tend to zero; this produces an overshoot by a factor of 1.1789797 and an undershoot by a factor of 0.9028233. A similar effect arises for a square-integrable nonperiodic function reconstructed from its Fourier transform. The phenomenon causes ringing around edges in low bit rate image coding. |
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