Gibbs phenomenon in tight framelet expansions
Source of Publication
Communications in Nonlinear Science and Numerical Simulation
© 2017 Elsevier B.V. In this paper, we explore several ways to investigate the Gibbs phenomenon in tight framelet representations. We present results concerning the Gibbs phenomenon by expanding functions using the quasi-affine system. This system is generated by the Haar tight framelets. More precisely, we investigate the existence of Gibbs phenomenon in the truncated expansion of a given function which is expanded by some tight framelet representation. The tight frame method is essentially a generalized wavelet based method. It provides various construction methods to expand functions in L2(R).
B-splines, Frames, Gibbs phenomenon, Quasi-affine system, Unitary extension principle (UEP), Wavelets
Mohammad, Mutaz and Lin, En Bing, "Gibbs phenomenon in tight framelet expansions" (2018). All Works. 1781.
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