Source of Publication
© 2019 by the authors. Gibbs effect represents the non-uniform convergence of the nth Fourier partial sums in approximating functions in the neighborhood of their non-removable discontinuities (jump discontinuities). The overshoots and undershoots cannot be removed by adding more terms in the series. This effect has been studied in the literature for wavelet and framelet expansions. Dual tight framelets have been proven useful in signal processing and many other applications where translation invariance, or the resulting redundancy, is very important. In this paper, we will study this effect using the dual tight framelets system. This system is generated by the mixed oblique extension principle. We investigate the existence of the Gibbs effect in the truncated expansion of a given function by using some dual tight framelets representation. We also give some examples to illustrate the results.
B-splines, Dual tight framelets, Gibbs phenomenon, Oblique extension principle, Quasi-affine, Shift-invariant system
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This work is licensed under a Creative Commons Attribution 4.0 International License.
Mohammad, Mutaz, "On the gibbs effect based on the quasi-affine dual tight framelets system generated using the mixed oblique extension principle" (2019). All Works. 2563.
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Gold: This publication is openly available in an open access journal/series