**4. Conclusions**

According to the above results, we show that the Gibbs effect is absent when the dual tight framelets of vanishing moments of order one are used to represent a function with jump discontinuities at the origin. Please note that increasing the vanishing moments, e.g., using the MOEP, will increase the approximation order of the framelet representation Q*n f* that used to expand the function *f* ; however, the Gibbs effects cannot be avoided for any level of *n*. Quite a few examples of dual tight framelets, numerical results, and graphical illustrations have been presented for the absence and presence of Gibbs effect.

**Funding:** This research was funded by Zayed University Research Fund.

**Acknowledgments:** I would like to thank the anonymous reviewers for their valuable comments to improve the quality of the paper.

**Conflicts of Interest:** The author declares no conflict of interest.
