Gibbs Phenomenon

The persistent overshoot and oscillatory ringing near a jump discontinuity that occurs when approximating a piecewise‑smooth function by truncated Fourier series or other global spectral expansions; the overshoot does not vanish as the number of terms grows, although it narrows.

The persistent oscillatory overshoot and ringing that occur near a jump discontinuity when a function is approximated by a truncated global series or spectral expansion (e.g., Fourier series); the overshoot approaches a finite fraction of the jump and does not vanish with truncation number.