@inbook{464a4779efe94356b84913f2600b6dc6,
title = "Gibbs effects using Daubechies and Coiflet tight framelet systems",
abstract = "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.",
keywords = "Coiflets, Daubechies wavelets, Gibbs phenomenon, Tight wavelet frames, Unitary extension principle",
author = "Mutaz Mohammad and Lin, {En Bing}",
note = "Funding Information: The first author was supported by the PD Grant, Research Office, Zayed University. The authors would like to thank Professor Susan Kelly from the University of Wisconsin-La Crosse for her helpful comments. We are very grateful to the anonymous referee{\textquoteright}s valuable comments and suggestions. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",
year = "2018",
doi = "10.1090/conm/706/14209",
language = "English",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "271--282",
booktitle = "Contemporary Mathematics",
}