Gibbs phenomenon in tight framelet expansions

Mutaz Mohammad, En Bing Lin

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

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).

Original languageEnglish
Pages (from-to)84-92
Number of pages9
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume55
DOIs
StatePublished - Feb 2018

Keywords

  • B-splines
  • Frames
  • Gibbs phenomenon
  • Quasi-affine system
  • Unitary extension principle (UEP)
  • Wavelets

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