The non-uniform convergence of the Fourier series for discontinuous functions is known as the Gibbs phenomenon. In 1899 American mathematician Josiah Willard Gibbs noticed that near a point where a function has a jump discontinuity, the partial sums of...

In mathematics, the Gibbs phenomenon (also known as ringing artifacts), named after the American physicist J. Willard Gibbs, is the peculiar manner in which the Fourier series of a piecewise continuously differentiable periodic function f behaves at a...