Gibbs effects using Daubechies and Coiflet tight framelet systems

Author First name, Last name, Institution

Mutaz Mohammad, Zayed University
En Bing Lin, Central Michigan University

Document Type

Article

Source of Publication

Contemporary Mathematics

Publication Date

1-1-2018

Abstract

© 2018 American Mathematical Society. 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.

DOI Link

10.1090/conm/706/14209

ISSN

0271-4132

Publisher

American Mathematical Society

Volume

706

First Page

271

Last Page

282

Disciplines

Physical Sciences and Mathematics

Keywords

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

Scopus ID

85049894926

Recommended Citation

Mohammad, Mutaz and Lin, En Bing, "Gibbs effects using Daubechies and Coiflet tight framelet systems" (2018). All Works. 1780.
https://zuscholars.zu.ac.ae/works/1780

Indexed in Scopus

yes

Open Access

no