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Reconstruction of analytic signal in Sobolev space by framelet sampling approximation
Li, Youfa1; Qian, Tao2
2018
Source PublicationAPPLICABLE ANALYSIS
ISSN0003-6811
Volume97Issue:2Pages:194-209
Abstract

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
DOIhttp://doi.org/10.1080/00036811.2016.1258115
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000426894400005
PublisherTAYLOR & FRANCIS LTD
The Source to ArticleWOS
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Citation statistics
Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
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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