Title

Gibbs effects using Daubechies and Coiflet tight framelet systems

Source of Publication

Contemporary Mathematics

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.

Document Type

Article

Publisher

American Mathematical Society

First Page

271

Last Page

282

Publication Date

1-1-2018

DOI

10.1090/conm/706/14209

Scopus ID

85049894926

This document is currently not available here.

Share

COinS