In this paper, we explore several ways to investigate the Gibbs phenomenon in tight framelet representations. We present results concerning the Gibbs phenomenon by expanding functions using the quasi-affine system. This system is generated by the Haar tight framelets. More precisely, we investigate the existence of Gibbs phenomenon in the truncated expansion of a given function which is expanded by some tight framelet representation. The tight frame method is essentially a generalized wavelet based method. It provides various construction methods to expand functions in L2(R).
|Number of pages||9|
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|State||Published - Feb 2018|
- Gibbs phenomenon
- Quasi-affine system
- Unitary extension principle (UEP)