Shannon-type sampling for multivariate non-bandlimited signals
Chen Q.H.1; Qian T.2; Li Y.F.3
Source PublicationScience China Mathematics

In this paper, starting from a function analytic in a neighborhood of the unit disk and based on Bessel functions, we construct a family of generalized multivariate sinc functions, which are radial and named radial Bessel-sinc (RBS) functions being time-frequency atoms with nonlinear phase. We obtain a recursive formula for the RBS functions in ℝ with d being odd. Based on the RBS function, a corresponding sampling theorem for a class of non-bandlimited signals is established. We investigate a class of radial functions and prove that each of these functions can be extended to become a monogenic function between two parallel planes, where the monogencity is taken to be of the Clifford analysis sense. 

KeywordAnalytic Function Fourier Transform Radial Bessel-sinc Function Shannon Sampling
URLView the original
Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000323437100013
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorLi Y.F.
Affiliation1.Cisco School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006, China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
3.College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China
Recommended Citation
GB/T 7714
Chen Q.H.,Qian T.,Li Y.F.. Shannon-type sampling for multivariate non-bandlimited signals[J]. Science China Mathematics,2013,56(9):1915-1934.
APA Chen Q.H.,Qian T.,&Li Y.F..(2013).Shannon-type sampling for multivariate non-bandlimited signals.Science China Mathematics,56(9),1915-1934.
MLA Chen Q.H.,et al."Shannon-type sampling for multivariate non-bandlimited signals".Science China Mathematics 56.9(2013):1915-1934.
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