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Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms
Chen Q.1,2; Qian T.3
Source PublicationApplicable Analysis
ISSN00036811 1563504X

This study concerns some new developments of unit analytic signals with non-linear phase. It includes ladder-shaped filter, generalized Sinc function based on non-linear Fourier atoms, generalized sampling theorem for nonbandlimited signals and the notion of multi-scale spectrum for discrete sequences. We first introduce the ladder-shaped filter and show that the impulse response of its corresponding linear time-shift invariant system is the generalized Sinc function as a product of periodic Poisson kernel and Sinc function. Secondly, we establish a Shannon-type sampling theorem based on generalized Sinc function for this type of non-bandlimited signal. We further prove that this type of signal may be holomorphically extended to strips in the complex plane containing the real axis. Finally, we introduce the notion of multi-scale spectrums for discrete sequences and develop the related fast algorithm. 

KeywordFourier Atoms Moebius Transform Shannon Sampling Sinc Function
URLView the original
Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000268701700007
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Cited Times [WOS]:13   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510420, P. R. China
2.Department of Mathematics, University of Aveiro, Aveiro 3810-193, Portugal
3.Department of Mathematics, University of Macau, Macao via Hong Kong, China
Recommended Citation
GB/T 7714
Chen Q.,Qian T.. Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms[J]. Applicable Analysis,2009,88(6):903-919.
APA Chen Q.,&Qian T..(2009).Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms.Applicable Analysis,88(6),903-919.
MLA Chen Q.,et al."Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms".Applicable Analysis 88.6(2009):903-919.
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