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Sparse reconstruction of Hardy signal and applications to time-frequency distribution
Qian T.; Li S.; Mai W.
2013-05-01
Source PublicationInternational Journal of Wavelets, Multiresolution and Information Processing
ISSN0219-6913
Volume11Issue:3
Abstract

In this paper, we introduce a sparse recovery strategy for analytic signals in Hardy space H(D), where D denotes the unit disk of the complex plane. The representation strategy is based on the optimization technique. We investigate the asymptotic singular values distribution of the dictionary matrix and give an estimation of the number of rows of the random matrix. To the best of our knowledge, this is the first time that such result is given. This result demonstrates that the dictionary of the normalized Szegö kernels (or reproducing kernels) is perfect for decompositions of analytic signals. A numerical example is presented exhibiting the theory. As applications, we still work on time-frequency analysis and propose a new type of non-negative time-frequency distribution associated with mono-components in the periodic case.

KeywordAnalytic Signal Hardy Space Singular Value Sparse Representation Time-frequency Distribution
DOIhttps://doi.org/10.1142/S0219691313500318
URLView the original
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000319995600010
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
AffiliationDepartment of Mathematics, University of Macau, Macau
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Qian T.,Li S.,Mai W.. Sparse reconstruction of Hardy signal and applications to time-frequency distribution[J]. International Journal of Wavelets, Multiresolution and Information Processing,2013,11(3).
APA Qian T.,Li S.,&Mai W..(2013).Sparse reconstruction of Hardy signal and applications to time-frequency distribution.International Journal of Wavelets, Multiresolution and Information Processing,11(3).
MLA Qian T.,et al."Sparse reconstruction of Hardy signal and applications to time-frequency distribution".International Journal of Wavelets, Multiresolution and Information Processing 11.3(2013).
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