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.
