Digital computation of the weighted-type fractional Fourier transform
Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with cons...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Mei, Lin [verfasserIn] Zhang, QinYu [verfasserIn] Sha, XueJun [verfasserIn] Zhang, NaiTong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
fractional Fourier transform (FRFT) weighted-type fractional Fourier transform (WFRFT) chirptype fractional Fourier transform (CFRFT) |
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| Übergeordnetes Werk: |
Enthalten in: Science in China - Heidelberg : Springer, 2001, 56(2013), 7 vom: 02. Feb., Seite 1-12 |
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| Übergeordnetes Werk: |
volume:56 ; year:2013 ; number:7 ; day:02 ; month:02 ; pages:1-12 |
| Links: |
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| DOI / URN: |
10.1007/s11432-013-4818-5 |
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| Katalog-ID: |
SPR019311869 |
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| 520 | |a Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy %$ when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. | ||
| 650 | 4 | |a fractional Fourier transform (FRFT) |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a weighted-type fractional Fourier transform (WFRFT) |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a chirptype fractional Fourier transform (CFRFT) |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a discrete fractional Fourier transform |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a discrete Fourier transform (DFT) |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Zhang, QinYu |e verfasserin |4 aut | |
| 700 | 1 | |a Sha, XueJun |e verfasserin |4 aut | |
| 700 | 1 | |a Zhang, NaiTong |e verfasserin |4 aut | |
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10.1007/s11432-013-4818-5 doi (DE-627)SPR019311869 (SPR)s11432-013-4818-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Mei, Lin verfasserin aut Digital computation of the weighted-type fractional Fourier transform 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy %$ when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. fractional Fourier transform (FRFT) (dpeaa)DE-He213 weighted-type fractional Fourier transform (WFRFT) (dpeaa)DE-He213 chirptype fractional Fourier transform (CFRFT) (dpeaa)DE-He213 discrete fractional Fourier transform (dpeaa)DE-He213 discrete Fourier transform (DFT) (dpeaa)DE-He213 Zhang, QinYu verfasserin aut Sha, XueJun verfasserin aut Zhang, NaiTong verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 56(2013), 7 vom: 02. Feb., Seite 1-12 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:56 year:2013 number:7 day:02 month:02 pages:1-12 https://dx.doi.org/10.1007/s11432-013-4818-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 56 2013 7 02 02 1-12 |
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10.1007/s11432-013-4818-5 doi (DE-627)SPR019311869 (SPR)s11432-013-4818-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Mei, Lin verfasserin aut Digital computation of the weighted-type fractional Fourier transform 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy %$ when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. fractional Fourier transform (FRFT) (dpeaa)DE-He213 weighted-type fractional Fourier transform (WFRFT) (dpeaa)DE-He213 chirptype fractional Fourier transform (CFRFT) (dpeaa)DE-He213 discrete fractional Fourier transform (dpeaa)DE-He213 discrete Fourier transform (DFT) (dpeaa)DE-He213 Zhang, QinYu verfasserin aut Sha, XueJun verfasserin aut Zhang, NaiTong verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 56(2013), 7 vom: 02. Feb., Seite 1-12 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:56 year:2013 number:7 day:02 month:02 pages:1-12 https://dx.doi.org/10.1007/s11432-013-4818-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 56 2013 7 02 02 1-12 |
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10.1007/s11432-013-4818-5 doi (DE-627)SPR019311869 (SPR)s11432-013-4818-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Mei, Lin verfasserin aut Digital computation of the weighted-type fractional Fourier transform 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy %$ when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. fractional Fourier transform (FRFT) (dpeaa)DE-He213 weighted-type fractional Fourier transform (WFRFT) (dpeaa)DE-He213 chirptype fractional Fourier transform (CFRFT) (dpeaa)DE-He213 discrete fractional Fourier transform (dpeaa)DE-He213 discrete Fourier transform (DFT) (dpeaa)DE-He213 Zhang, QinYu verfasserin aut Sha, XueJun verfasserin aut Zhang, NaiTong verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 56(2013), 7 vom: 02. Feb., Seite 1-12 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:56 year:2013 number:7 day:02 month:02 pages:1-12 https://dx.doi.org/10.1007/s11432-013-4818-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 56 2013 7 02 02 1-12 |
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10.1007/s11432-013-4818-5 doi (DE-627)SPR019311869 (SPR)s11432-013-4818-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Mei, Lin verfasserin aut Digital computation of the weighted-type fractional Fourier transform 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy %$ when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. fractional Fourier transform (FRFT) (dpeaa)DE-He213 weighted-type fractional Fourier transform (WFRFT) (dpeaa)DE-He213 chirptype fractional Fourier transform (CFRFT) (dpeaa)DE-He213 discrete fractional Fourier transform (dpeaa)DE-He213 discrete Fourier transform (DFT) (dpeaa)DE-He213 Zhang, QinYu verfasserin aut Sha, XueJun verfasserin aut Zhang, NaiTong verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 56(2013), 7 vom: 02. Feb., Seite 1-12 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:56 year:2013 number:7 day:02 month:02 pages:1-12 https://dx.doi.org/10.1007/s11432-013-4818-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 56 2013 7 02 02 1-12 |
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10.1007/s11432-013-4818-5 doi (DE-627)SPR019311869 (SPR)s11432-013-4818-5-e DE-627 ger DE-627 rakwb eng 070 004 ASE 54.00 bkl Mei, Lin verfasserin aut Digital computation of the weighted-type fractional Fourier transform 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy %$ when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. fractional Fourier transform (FRFT) (dpeaa)DE-He213 weighted-type fractional Fourier transform (WFRFT) (dpeaa)DE-He213 chirptype fractional Fourier transform (CFRFT) (dpeaa)DE-He213 discrete fractional Fourier transform (dpeaa)DE-He213 discrete Fourier transform (DFT) (dpeaa)DE-He213 Zhang, QinYu verfasserin aut Sha, XueJun verfasserin aut Zhang, NaiTong verfasserin aut Enthalten in Science in China Heidelberg : Springer, 2001 56(2013), 7 vom: 02. Feb., Seite 1-12 (DE-627)385614764 (DE-600)2142898-0 1862-2836 nnns volume:56 year:2013 number:7 day:02 month:02 pages:1-12 https://dx.doi.org/10.1007/s11432-013-4818-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-BBI SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 54.00 ASE AR 56 2013 7 02 02 1-12 |
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Enthalten in Science in China 56(2013), 7 vom: 02. Feb., Seite 1-12 volume:56 year:2013 number:7 day:02 month:02 pages:1-12 |
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070 004 ASE 54.00 bkl Digital computation of the weighted-type fractional Fourier transform fractional Fourier transform (FRFT) (dpeaa)DE-He213 weighted-type fractional Fourier transform (WFRFT) (dpeaa)DE-He213 chirptype fractional Fourier transform (CFRFT) (dpeaa)DE-He213 discrete fractional Fourier transform (dpeaa)DE-He213 discrete Fourier transform (DFT) (dpeaa)DE-He213 |
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Digital computation of the weighted-type fractional Fourier transform |
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Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy %$ when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. |
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Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy %$ when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. |
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Abstract The paper reveals the time-frequency symmetric property of the weighted-type fractional Fourier transform (WFRFT) by investigating the original definition of the WFRFT, and proposes a discrete algorithm of the WFRFT based on the weighted discrete Fourier transform (WDFT) algorithm with constraint conditions of the definition of the WFRFT and time-domain sampling. When the WDFT is considered in digital computation of the WFRFT, the Fourier transform in the definition of the WFRFT should be defined in frequency (Hz) but not angular frequency (rad/s). The sampling period Δt and sampling duration T should satisfy %$ when N-point DFT is utilized. Since Hermite-Gaussian functions are the best known eigenfunctions of the fractional Fourier transform (FRFT), digital computation based on eigendecomposition is also carried out as the additional verification and validation for the WFRFT calculation. |
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