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FFT formulations of adaptive Fourier decomposition
Gao, You1; Ku, Min2; Qian, Tao1; Wang, Jianzhong3

Adaptive Fourier decomposition (AFD) has been found to be among the most effective greedy algorithms. AFD shows an outstanding performance in signal analysis and system identification. As compensation of effectiveness, the computation complexity is great, that is especially due to maximal selections of the parameters. In this paper, we explore the discretization of the 1-D AFD integration via with discrete Fourier transform (DFT), incorporating fast Fourier transform (FFT). We show that the new algorithm, called FFT-AFD, reduces the computational complexity from O (MN2) to O (MN log N), the latter being the same as FFT. Through experiments, we verify the effectiveness, accuracy, and robustness of the proposed algorithm. The proposed FFT-based algorithm for AFD lays a foundation for its practical applications. (C) 2017 Elsevier B.V. All rights reserved.

KeywordFast Fourier Transform Computational Complexity Adaptive Decomposition Greedy Algorithm Reproducing Kernel Hilbert Space
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Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000403633900012
The Source to ArticleWOS
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Cited Times [WOS]:11   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorGao, You; Ku, Min; Qian, Tao; Wang, Jianzhong
Affiliation1.Department of Mathematics, University of Macau, Macao
2.CIDMA, Department of Mathematics, University of Aveiro, Portugal
3.Department of Mathematics and Statistics, Sam Houston State University, United States
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Gao, You,Ku, Min,Qian, Tao,et al. FFT formulations of adaptive Fourier decomposition[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2017,324:204-215.
APA Gao, You,Ku, Min,Qian, Tao,&Wang, Jianzhong.(2017).FFT formulations of adaptive Fourier decomposition.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,324,204-215.
MLA Gao, You,et al."FFT formulations of adaptive Fourier decomposition".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 324(2017):204-215.
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