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Reconstruction of analytic signal in Sobolev space by framelet sampling approximation
Li, Youfa1; Qian, Tao2

Based on dual framelets, we construct the sampling approximation for the whole Sobolev space H-s(R) where s > 1/2. In particular, the sampling system has adjustable shift parameters. By the B-spline sampling system, we construct the approximation of Hilbert transform of any function of Hs(R). Combining the approximation of the function Hs(R) and that of its Hilbert transform, we establish a reconstruction method for the analytic signal. Particularly, the reconstruction series converges exponentially with respect to the scale level. Moreover, the numerical singularity emerging in computation of Hilbert transform can be removed by adjusting the shift parameters. That is, the method of reconstruction of analytic signal is numerically and L-2-stable. Several numerical experiments are carried out to check the efficiency of our reconstruction method.

KeywordAnalytic Signal Dual Framelets Sobolev Space Adjustable Sampling System Approximation Order Dnumerical Singularity
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Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000426894400005
The Source to ArticleWOS
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Corresponding AuthorLi, Youfa
Affiliation1.College of Mathematics and Information Science, Guangxi University, Nanning, P.R. China
2.Department of Mathematics, Macau University, Macao, P.R. China
Recommended Citation
GB/T 7714
Li, Youfa,Qian, Tao. Reconstruction of analytic signal in Sobolev space by framelet sampling approximation[J]. APPLICABLE ANALYSIS,2018,97(2):194-209.
APA Li, Youfa,&Qian, Tao.(2018).Reconstruction of analytic signal in Sobolev space by framelet sampling approximation.APPLICABLE ANALYSIS,97(2),194-209.
MLA Li, Youfa,et al."Reconstruction of analytic signal in Sobolev space by framelet sampling approximation".APPLICABLE ANALYSIS 97.2(2018):194-209.
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