Fast basis search for adaptive Fourier decomposition
Abstract The adaptive Fourier decomposition (AFD) uses an adaptive basis instead of a fixed basis in the rational analytic function and thus achieves a fast energy convergence rate. At each decomposition level, an important step is to determine a new basis element from a dictionary to maximize the e...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-12-01
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| Series: | EURASIP Journal on Advances in Signal Processing |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13634-018-0593-1 |
| _version_ | 1819034866026545152 |
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| author | Ze Wang Feng Wan Chi Man Wong Tao Qian |
| author_facet | Ze Wang Feng Wan Chi Man Wong Tao Qian |
| author_sort | Ze Wang |
| collection | DOAJ |
| description | Abstract The adaptive Fourier decomposition (AFD) uses an adaptive basis instead of a fixed basis in the rational analytic function and thus achieves a fast energy convergence rate. At each decomposition level, an important step is to determine a new basis element from a dictionary to maximize the extracted energy. The existing basis searching method, however, is only the exhaustive searching method that is rather inefficient. This paper proposes four methods to accelerate the AFD algorithm based on four typical optimization techniques including the unscented Kalman filter (UKF) method, the Nelder-Mead (NM) algorithm, the genetic algorithm (GA), and the particle swarm optimization (PSO) algorithm. In the simulation of decomposing four representative signals and real ECG signals, compared with the existing exhaustive search method, the proposed schemes can achieve much higher computation speed with a fast energy convergence, that is, in particular, to make the AFD possible for real-time applications. |
| first_indexed | 2024-12-21T07:40:32Z |
| format | Article |
| id | doaj.art-8631ce3d64414976b4be5c4a421393be |
| institution | Directory Open Access Journal |
| issn | 1687-6180 |
| language | English |
| last_indexed | 2024-12-21T07:40:32Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | EURASIP Journal on Advances in Signal Processing |
| spelling | doaj.art-8631ce3d64414976b4be5c4a421393be2022-12-21T19:11:19ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61802018-12-012018111410.1186/s13634-018-0593-1Fast basis search for adaptive Fourier decompositionZe Wang0Feng Wan1Chi Man Wong2Tao Qian3Department of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Avenida da UniversidadeDepartment of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Avenida da UniversidadeDepartment of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Avenida da UniversidadeDepartment of Mathematics, Faculty of Science and Technology, University of Macau, Avenida da UniversidadeAbstract The adaptive Fourier decomposition (AFD) uses an adaptive basis instead of a fixed basis in the rational analytic function and thus achieves a fast energy convergence rate. At each decomposition level, an important step is to determine a new basis element from a dictionary to maximize the extracted energy. The existing basis searching method, however, is only the exhaustive searching method that is rather inefficient. This paper proposes four methods to accelerate the AFD algorithm based on four typical optimization techniques including the unscented Kalman filter (UKF) method, the Nelder-Mead (NM) algorithm, the genetic algorithm (GA), and the particle swarm optimization (PSO) algorithm. In the simulation of decomposing four representative signals and real ECG signals, compared with the existing exhaustive search method, the proposed schemes can achieve much higher computation speed with a fast energy convergence, that is, in particular, to make the AFD possible for real-time applications.http://link.springer.com/article/10.1186/s13634-018-0593-1Adaptive Fourier decompositionUnscented Kalman filterNelder-Mead algorithmGenetic algorithmParticle swarm optimization algorithm |
| spellingShingle | Ze Wang Feng Wan Chi Man Wong Tao Qian Fast basis search for adaptive Fourier decomposition EURASIP Journal on Advances in Signal Processing Adaptive Fourier decomposition Unscented Kalman filter Nelder-Mead algorithm Genetic algorithm Particle swarm optimization algorithm |
| title | Fast basis search for adaptive Fourier decomposition |
| title_full | Fast basis search for adaptive Fourier decomposition |
| title_fullStr | Fast basis search for adaptive Fourier decomposition |
| title_full_unstemmed | Fast basis search for adaptive Fourier decomposition |
| title_short | Fast basis search for adaptive Fourier decomposition |
| title_sort | fast basis search for adaptive fourier decomposition |
| topic | Adaptive Fourier decomposition Unscented Kalman filter Nelder-Mead algorithm Genetic algorithm Particle swarm optimization algorithm |
| url | http://link.springer.com/article/10.1186/s13634-018-0593-1 |
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