Special B-spline Tight Framelet and It's Applications
Mutaz Mohammad *
Zayed University, Abu Dhabi, UAE.
En-Bing Lin
Central Michigan University, Mount Pleasant, Michigan 48859, USA.
Amer Darweesh
Jordan University of Science and Technology, Irbid, Jordan.
Fares Howari
Zayed University, Abu Dhabi, UAE.
*Author to whom correspondence should be addressed.
Abstract
We present a special B-spline tight frame and use it to introduce our numerical approximation method. We apply our method to investigate Gibbs effects and illustrate some features of the associated framelet expansion. It is shown that Gibbs effects occurs in the framelet expansion of a function with a jump discontinuity at 0 for certain classes of framelets. Numerical results are obtained regarding the behavior of the Gibbs effects. We present the results by expanding functions using the quasi-ane system. This system is generated by the B-spline tight framelets with a specific number of generators. We show numerically the existence of Gibbs effects in the truncated expansion of a given function by using some tight framelet representation.
Keywords: Gibbs phenomenon, Tight frames, Unitary extension principle (UEP), Quasi-ane system, B-splines