UM
Phase Derivative of Monogenic Signals in Higher Dimensional Spaces
Yang Y.1; Qian T.2; Sommen F.3
2012-10-01
Source PublicationComplex Analysis and Operator Theory
ISSN16618254 16618262
Volume6Issue:5Pages:987-1010
Abstract

In the Clifford algebra setting of a Euclidean space on the boundary of a domain it is natural to define a monogenic (analytic) signal to be the boundary value of a monogenic (analytic) function inside the domain. The question is how to define a canonical phase and, correspondingly, a phase derivative. In this paper we give an answer to these questions in the unit ball and in the upper-half space. Among the possible candidates of phases and phase derivatives we decided that the right ones are those that give rise to, as in the one dimensional signal case, the equal relations between the mean of the Fourier frequency and the mean of the phase derivative, and the positivity of the phase derivative of the shifted Cauchy kernel.

KeywordFrequency Möbius Transforms Monogenic Signals Poisson Kernel
DOIhttps://doi.org/10.1007/s11785-011-0210-x
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000310225000002
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Cited Times [WOS]:10   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao, China
3.Faculty of Engineering, Ghent University, Ghent, Belgium
Recommended Citation
GB/T 7714
Yang Y.,Qian T.,Sommen F.. Phase Derivative of Monogenic Signals in Higher Dimensional Spaces[J]. Complex Analysis and Operator Theory,2012,6(5):987-1010.
APA Yang Y.,Qian T.,&Sommen F..(2012).Phase Derivative of Monogenic Signals in Higher Dimensional Spaces.Complex Analysis and Operator Theory,6(5),987-1010.
MLA Yang Y.,et al."Phase Derivative of Monogenic Signals in Higher Dimensional Spaces".Complex Analysis and Operator Theory 6.5(2012):987-1010.
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