Bi-orthogonal wavelets for investigating Gibbs effects via oblique extension principle

Abstract

Gibbs effect is generally known for Fourier and Wavelets expansions of a function in the neighborhood of its discontinuities points which deals with the nonuniform convergence of its truncated sums of these expansions. We study this phenomenon using bi-orthogonal wavelets (or simply, framelets) using pseudo-spline tight framelets generated using the oblique extension principle. We present some examples to illustrate the results.