A summability for Meyer wavelets

Shim, Hong-Tae; Jung, Kap Hun

doi:10.1007/bf03021556

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Gibbs Effect In Quasi-affine Dual Tight Framelet Expansions1

Introduction1

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2019

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“…Now, the proof is completed by taking B → ∞ and using Equations (6) and (13). Thus, we have Now, we present some examples of dual tight framelets constructed by the MOEP in Ref.…”

Section: Gibbs Effect In Quasi-affine Dual Tight Framelet Expansionsmentioning

confidence: 99%

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On the Gibbs Effect Based on the Quasi-Affine Dual Tight Framelets System Generated Using the Mixed Oblique Extension Principle

Mohammad

2019

Mathematics

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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.

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“…Now, the proof is completed by taking B → ∞ and using Equations (6) and (13). Thus, we have Now, we present some examples of dual tight framelets constructed by the MOEP in Ref.…”

Section: Gibbs Effect In Quasi-affine Dual Tight Framelet Expansionsmentioning

confidence: 99%

“…This phenomenon has been studied extensively in Fourier series and many other situations such as the classical orthogonal expansions (see Refs. [6][7][8]), spline expansion (see Refs. [9,10]), wavelets and framelets series (see Refs.…”

Section: Introductionmentioning

confidence: 99%

On the Gibbs Effect Based on the Quasi-Affine Dual Tight Framelets System Generated Using the Mixed Oblique Extension Principle

Mohammad

2019

Mathematics

View full text Add to dashboard Cite

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A summability for Meyer wavelets

Cited by 1 publication

References 4 publications

On the Gibbs Effect Based on the Quasi-Affine Dual Tight Framelets System Generated Using the Mixed Oblique Extension Principle

On the Gibbs Effect Based on the Quasi-Affine Dual Tight Framelets System Generated Using the Mixed Oblique Extension Principle

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