Gibbs effects using Daubechies and Coiflet tight framelet systems

Mutaz Mohammad, En Bing Lin

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

14 Scopus citations


In this article, we study the Gibbs phenomenon for compactly supported framelets, such as Daubechies and Coiflets framelets to illustrate the Gibbs effect. The tight framelets representation of a square integrable function is essentially a generalized wavelet representation. We show a numerical evidence that there is no Gibbs phenomenon when we exhibit the framelets expansion for a square integrable function by using 1st order Daubechies tight framelets for two generators. The investigation of Gibbs phenomenon in Daubechies tight framelets, however, shows that it exists for higher order. Also, we provide a numerical values of the overshoots and undershoots when we use Coiflets tight frame representation.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages12
StatePublished - 2018

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


  • Coiflets
  • Daubechies wavelets
  • Gibbs phenomenon
  • Tight wavelet frames
  • Unitary extension principle


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