Fast Linear Canonical Transform for Nonequispaced Data
The investigations of the discrete and fast linear canonical transform (LCT) are becoming one of the hottest research topics in modern signal processing and optics. Among them, the fast calculation of LCT for non-uniform data is one of key problems. Focus on this problem, a new fast algorithm of the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/5/353 |
| _version_ | 1797600025114574848 |
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| author | Yannan Sun Wenchao Qian |
| author_facet | Yannan Sun Wenchao Qian |
| author_sort | Yannan Sun |
| collection | DOAJ |
| description | The investigations of the discrete and fast linear canonical transform (LCT) are becoming one of the hottest research topics in modern signal processing and optics. Among them, the fast calculation of LCT for non-uniform data is one of key problems. Focus on this problem, a new fast algorithm of the LCT has been proposed in this paper firstly by interpolation and approximation theory. The proposed algorithms can calculate quickly the LCT of the data, whether the input or output data is uniform. Secondly, the complexity and precision of derived algorithms have been analyzed for different situations. Finally, the experimental results are presented to verify the correctness of the obtained results. |
| first_indexed | 2024-03-11T03:43:36Z |
| format | Article |
| id | doaj.art-64d757073e59464fafa7c0bb010f24fd |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T03:43:36Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-64d757073e59464fafa7c0bb010f24fd2023-11-18T01:25:55ZengMDPI AGFractal and Fractional2504-31102023-04-017535310.3390/fractalfract7050353Fast Linear Canonical Transform for Nonequispaced DataYannan Sun0Wenchao Qian1School of Mathematics, Jiangsu University, Zhenjiang 212013, ChinaSchool of Mathematics, Jiangsu University, Zhenjiang 212013, ChinaThe investigations of the discrete and fast linear canonical transform (LCT) are becoming one of the hottest research topics in modern signal processing and optics. Among them, the fast calculation of LCT for non-uniform data is one of key problems. Focus on this problem, a new fast algorithm of the LCT has been proposed in this paper firstly by interpolation and approximation theory. The proposed algorithms can calculate quickly the LCT of the data, whether the input or output data is uniform. Secondly, the complexity and precision of derived algorithms have been analyzed for different situations. Finally, the experimental results are presented to verify the correctness of the obtained results.https://www.mdpi.com/2504-3110/7/5/353linear canonical transformfast fourier transforminterpolationapproximation theorylinear canonical series |
| spellingShingle | Yannan Sun Wenchao Qian Fast Linear Canonical Transform for Nonequispaced Data Fractal and Fractional linear canonical transform fast fourier transform interpolation approximation theory linear canonical series |
| title | Fast Linear Canonical Transform for Nonequispaced Data |
| title_full | Fast Linear Canonical Transform for Nonequispaced Data |
| title_fullStr | Fast Linear Canonical Transform for Nonequispaced Data |
| title_full_unstemmed | Fast Linear Canonical Transform for Nonequispaced Data |
| title_short | Fast Linear Canonical Transform for Nonequispaced Data |
| title_sort | fast linear canonical transform for nonequispaced data |
| topic | linear canonical transform fast fourier transform interpolation approximation theory linear canonical series |
| url | https://www.mdpi.com/2504-3110/7/5/353 |
| work_keys_str_mv | AT yannansun fastlinearcanonicaltransformfornonequispaceddata AT wenchaoqian fastlinearcanonicaltransformfornonequispaceddata |