Optimal design of orders of DFrFTs for sparse representations
This study proposes an optimal design of the orders of the discrete fractional Fourier transforms (DFrFTs) and construct an overcomplete transform using the DFrFTs with these orders for performing the sparse representations. The design problem is formulated as an optimisation problem with an L1-norm...
| Main Authors: | , , , , , , |
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| Format: | Journal Article |
| Published: |
The Institution of Engineering and Technology
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/71859 |
| _version_ | 1848762591624560640 |
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| author | Zhang, X. Ling, B. Tao, R. Yang, Z. Woo, W. Sanei, S. Teo, Kok Lay |
| author_facet | Zhang, X. Ling, B. Tao, R. Yang, Z. Woo, W. Sanei, S. Teo, Kok Lay |
| author_sort | Zhang, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This study proposes an optimal design of the orders of the discrete fractional Fourier transforms (DFrFTs) and construct an overcomplete transform using the DFrFTs with these orders for performing the sparse representations. The design problem is formulated as an optimisation problem with an L1-norm non-convex objective function. To avoid all the orders of the DFrFTs to be the same, the exclusive OR of two constraints are imposed. The constrained optimisation problem is further reformulated to an optimal frequency sampling problem. A method based on solving the roots of a set of harmonic functions is employed for finding the optimal sampling frequencies. As the designed overcomplete transform can exploit the physical meanings of the signals in terms of representing the signals as the sums of the components in the time-frequency plane, the designed overcomplete transform can be applied to many applications. |
| first_indexed | 2025-11-14T10:50:00Z |
| format | Journal Article |
| id | curtin-20.500.11937-71859 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:50:00Z |
| publishDate | 2018 |
| publisher | The Institution of Engineering and Technology |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-718592019-03-27T02:04:46Z Optimal design of orders of DFrFTs for sparse representations Zhang, X. Ling, B. Tao, R. Yang, Z. Woo, W. Sanei, S. Teo, Kok Lay This study proposes an optimal design of the orders of the discrete fractional Fourier transforms (DFrFTs) and construct an overcomplete transform using the DFrFTs with these orders for performing the sparse representations. The design problem is formulated as an optimisation problem with an L1-norm non-convex objective function. To avoid all the orders of the DFrFTs to be the same, the exclusive OR of two constraints are imposed. The constrained optimisation problem is further reformulated to an optimal frequency sampling problem. A method based on solving the roots of a set of harmonic functions is employed for finding the optimal sampling frequencies. As the designed overcomplete transform can exploit the physical meanings of the signals in terms of representing the signals as the sums of the components in the time-frequency plane, the designed overcomplete transform can be applied to many applications. 2018 Journal Article http://hdl.handle.net/20.500.11937/71859 10.1049/iet-spr.2017.0283 The Institution of Engineering and Technology restricted |
| spellingShingle | Zhang, X. Ling, B. Tao, R. Yang, Z. Woo, W. Sanei, S. Teo, Kok Lay Optimal design of orders of DFrFTs for sparse representations |
| title | Optimal design of orders of DFrFTs for sparse representations |
| title_full | Optimal design of orders of DFrFTs for sparse representations |
| title_fullStr | Optimal design of orders of DFrFTs for sparse representations |
| title_full_unstemmed | Optimal design of orders of DFrFTs for sparse representations |
| title_short | Optimal design of orders of DFrFTs for sparse representations |
| title_sort | optimal design of orders of dfrfts for sparse representations |
| url | http://hdl.handle.net/20.500.11937/71859 |