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Adaptive Fourier decomposition‐based Dirac type time‐frequency distribution
Author(s) -
Zhang Liming,
Qian Tao,
Mai Weixiong,
Dang Pei
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4199
Subject(s) - fourier transform , type (biology) , mathematics , time–frequency analysis , representation (politics) , decomposition , dirac (video compression format) , wigner distribution function , ideal (ethics) , distribution (mathematics) , time–frequency representation , algorithm , pure mathematics , mathematical analysis , computer science , quantum mechanics , physics , epistemology , telecommunications , ecology , radar , philosophy , neutrino , politics , political science , law , quantum , biology
The Dirac‐type time‐frequency distribution (TFD), regarded as ideal TFD, has long been desired. It, until the present time, cannot be implemented, due to the fact that there has been no appropriate representation of signals leading to such TFD. Instead, people have been developing other types of TFD, including the Wigner and the windowed Fourier transform types. This paper promotes a practical passage leading to a Dirac‐type TFD. Based on the proposed function decomposition method, viz., adaptive Fourier decomposition, we establish a rigorous and practical Dirac‐type TFD theory. We do follow the route of analytic signal representation of signals founded and developed by Garbo, Ville, Cohen, Boashash, Picinbono, and others. The difference, however, is that our treatment is theoretically throughout and rigorous. To well illustrate the new theory and the related TFD, we include several examples and experiments of which some are in comparison with the most commonly used TFDs. Copyright © 2016 John Wiley & Sons, Ltd.