The Gibbs phenomenon is the signal-processing law that explains ringing. Reconstruct any sharp jump from a limited band of frequencies and the result cannot stay flat on either side: it overshoots just past the jump, dips back, overshoots again less, and oscillates its way to calm. The striking part is that the overshoot settles at a fixed proportion of the jump height - about 9% (precisely near 8.95%) - no matter how many frequencies you keep; adding more makes the ripples tighter to the edge but never shorter. This is exactly what a codec does to an edge: the DCT packs the edge's energy into high-frequency coefficients, quantization rounds those away, and the decoder rebuilds the edge from too few frequencies, so it overshoots and rings. A mid-contrast edge stepping by 128 code values shows an overshoot of about 11 code values beside it. The literature distinguishes the first bump (overshoot) from the decaying ripples that follow (ringing); a little overshoot is also how sharpening makes edges look crisp.
The handbook · 7 volumes
Fora Soft Video Engineering Handbook
The Gibbs phenomenon is why sharp edges ring after compression: dropping high frequencies leaves an overshoot that more bits only narrow. We wrote seven volumes covering the whole video stack, and for the Gibbs phenomenon start with Volume 1: transforms and frequency, quantization, ringing and mosquito noise in H.264, HEVC and AV1. Written by Nikolay Sapunov, CEO at Fora Soft.
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