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Volumn 44, Issue 9, 1996, Pages 2141-2150

Digital computation of the fractional fourier transform

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BANDWIDTH; CALCULATIONS; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; NUMERICAL METHODS;

EID: 0030243105     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.536672     Document Type: Article
Times cited : (1219)

References (45)
  • 1
    • 0028382656 scopus 로고
    • Convolution filtering, and multiplexing in fractional Fourier domains and thei relation to chirp and wavelet transforms'
    • H. M. Ozaktas, B. Barshan, D. Mendlovic. and L. Onural, "Convolution filtering, and multiplexing in fractional Fourier domains and thei relation to chirp and wavelet transforms,'' J. Opt, Soc. Amer. A, vol 11, pp. 547-559, 1994.
    • (1994) J. Opt, Soc. Amer. a , vol.11 , pp. 547-559
    • Ozaktas, H.M.1    Barshan, B.2    Mendlovic, D.3    Onural, L.4
  • 2
    • 77958407025 scopus 로고
    • The fractional Fourier transform and its application i quantum mechanics
    • V. Namias, "The fractional Fourier transform and its application i quantum mechanics," J. Insl. Maths. Application, vol. 25, pp. 241-265 1980.
    • (1980) J. Insl. Maths. Application , vol.25 , pp. 241-265
    • Namias, V.1
  • 3
    • 77957689582 scopus 로고
    • On Namias's fractional Fourie transform
    • A. C. McBride and F. H. Kerr, "On Namias's fractional Fourie transform," IMA J. Applied Math., vol. 39, pp. 159-175, 1987.
    • (1987) IMA J. Applied Math. , vol.39 , pp. 159-175
    • McBride, A.C.1    Kerr, F.H.2
  • 4
    • 0028546458 scopus 로고
    • The fractional Fourier transform and time-frequenc representations
    • Nov.
    • L. B. Almeida, "The fractional Fourier transform and time-frequenc representations," IEEE Trans. Signal Processing, vol. 42, pp 3084-3091,Nov. 1994.
    • (1994) IEEE Trans. Signal Processing , vol.42 , pp. 3084-3091
    • Almeida, L.B.1
  • 5
    • 23544460852 scopus 로고
    • Determination of quasiprobability distribution in terms of probability distributions for the rotated quadrature phase
    • K. Vogel and H. Risken, "Determination of quasiprobability distribution in terms of probability distributions for the rotated quadrature phase, Phys. Rev. A, vol. 40, pp. 2847-2849, 1989.
    • (1989) Phys. Rev. A , vol.40 , pp. 2847-2849
    • Vogel, K.1    Risken, H.2
  • 6
    • 0000563312 scopus 로고
    • Quantum superpositio generated by quantum nondemolition measurements."
    • B. Yurke, W. Schleich, and D. F. Walk, "Quantum superpositio generated by quantum nondemolition measurements." Phvs. Rev. A. vol 42, pp. 1703-1711, 1990.
    • (1990) Phvs. Rev. A. , vol.42 , pp. 1703-1711
    • Yurke, B.1    Schleich, W.2    Walk, D.F.3
  • 7
    • 0000442750 scopus 로고
    • Phase distribution of a quantum stat without using phase states
    • W. Vogel and W. Schleich, "Phase distribution of a quantum stat without using phase states," Phys. Rev. A, vol. 44, pp. 7642-7646, 1991.
    • (1991) Phys. Rev. A , vol.44 , pp. 7642-7646
    • Vogel, W.1    Schleich, W.2
  • 8
    • 0027560182 scopus 로고
    • Measuremen of the Wigner distribution and the density matrix of a light mode usin optical homodyne tomography: Application to squeezed states and th vacuum
    • D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridanil, "Measuremen of the Wigner distribution and the density matrix of a light mode usin optical homodyne tomography: Application to squeezed states and th vacuum," Phys. Rev. Lett., vol. 70, pp. 1244-1247, 1993.
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 1244-1247
    • Smithey, D.T.1    Beck, M.2    Raymer, M.G.3    Faridanil, A.4
  • 9
    • 0027707727 scopus 로고
    • Chronocycli tomography for measuring the amplitude and phase structure of optica pulses
    • M. Beck, M. G. Raymer, I. A. Walmsley. and V. Kong, "Chronocycli tomography for measuring the amplitude and phase structure of optica pulses," Opt. Le., vol. 18, pp. 2041-2043, 1993.
    • (1993) Opt. Le. , vol.18 , pp. 2041-2043
    • Beck, M.1    Raymer, M.G.2    Walmsley, I.A.3    Kong, V.4
  • 10
    • 12044254133 scopus 로고
    • Complex wave-fiel reconstruction using phase-space tomography
    • M. G. Raymer, M. Beck, and D. F. McAlister, "Complex wave-fiel reconstruction using phase-space tomography," Phys. Rev. Lett., vol 72, pp. 1137-1140, 1994
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 1137-1140
    • Raymer, M.G.1    Beck, M.2    McAlister, D.F.3
  • 11
    • 75249106441 scopus 로고
    • Spatial and temporal optical field reconstruction using phasespace tomography."
    • J. D. Harvey and D. F. Wall Eds. Berlin: Springer-Verlag
    • _, "Spatial and temporal optical field reconstruction using phasespace tomography." Quantum Optics VI. J. D. Harvey and D. F. Wall Eds. Berlin: Springer-Verlag, 1994.
    • (1994) Quantum Optics VI.
  • 12
    • 0028483920 scopus 로고
    • A simple realization of fractional Fourie transform and relation to harmonic oscillator Green's function
    • G. S. Agarwal and R. Simon, "A simple realization of fractional Fourie transform and relation to harmonic oscillator Green's function," Opt Commun., vol. 110, pp. 23-26, 1994.
    • (1994) Opt Commun. , vol.110 , pp. 23-26
    • Agarwal, G.S.1    Simon, R.2
  • 13
    • 33747722913 scopus 로고
    • Fourier transform of fractional order and their optical interpretation
    • Washington, DC. OSA Tech. Digest Series, Opt Soc. Amer.
    • D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, "Fourier transform of fractional order and their optical interpretation," in Proc. Topical Mtg Optical Compul, Washington, DC. 1993, OSA Tech. Digest Series, Opt Soc. Amer. pp. 127-130.
    • (1993) Proc. Topical Mtg Optical Compul , pp. 127-130
    • Mendlovic, D.1    Ozaktas, H.M.2    Lohmann, A.W.3
  • 14
    • 0027641018 scopus 로고
    • Fourier transforms of fractional orde and their optical interpretation
    • H. M. Ozaktas and D. Mendlovic, "Fourier transforms of fractional orde and their optical interpretation," Opt. Commun., vol. 101, pp. 163-169 1993.
    • (1993) Opt. Commun. , vol.101 , pp. 163-169
    • Ozaktas, H.M.1    Mendlovic, D.2
  • 15
    • 0027652515 scopus 로고
    • Fractional Fourier transformation and their optical implementation: Part 1
    • D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transformation and their optical implementation: Part 1," J. Opt. Soc. Amer. A, vol. 10 pp. 1875-1881, 1993.
    • (1993) J. Opt. Soc. Amer. A , vol.10 , pp. 1875-1881
    • Mendlovic, D.1    Ozaktas, H.M.2
  • 16
    • 0027740848 scopus 로고
    • Fractional Fourier transformation and their optical implementation: Part II
    • H. M. Ozaktas and D. Mendlovic, "Fractional Fourier transformation and their optical implementation: Part II," J, Opt. Sac. Amer. A, vol. 10 pp. 2522-2531, 1993.
    • (1993) J, Opt. Sac. Amer. A , vol.10 , pp. 2522-2531
    • Ozaktas, H.M.1    Mendlovic, D.2
  • 17
    • 0027682286 scopus 로고
    • Image rotation, Wigner rotation and the fractiona Fourier transform
    • A. W. Lohmann, "Image rotation, Wigner rotation and the fractiona Fourier transform," J. Opt. Soc. Amer. A. vol. 10, pp. 2181-2186, 1993.
    • (1993) J. Opt. Soc. Amer. A. , vol.10 , pp. 2181-2186
    • Lohmann, A.W.1
  • 18
    • 33747678255 scopus 로고    scopus 로고
    • The effec of propagation in graded index media on the Wigner distributio function and the equivalence of two definitions of the fractional Fourier transform
    • to appear
    • D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, "The effec of propagation in graded index media on the Wigner distributio function and the equivalence of two definitions of the fractional Fourier transform," to appear in Appl. Opt.
    • Appl. Opt.
    • Mendlovic, D.1    Ozaktas, H.M.2    Lohmann, A.W.3
  • 19
    • 0028546549 scopus 로고
    • The fractional Fourier transform a a tool for analyzing beam propagation and spherical mirror resonators
    • Nov.
    • H. M. Ozaktas and D. Mendlovic, ''The fractional Fourier transform a a tool for analyzing beam propagation and spherical mirror resonators, Opt. Lett.,Nov. 1994.
    • (1994) Opt. Lett.
    • Ozaktas, H.M.1    Mendlovic, D.2
  • 20
    • 0029292376 scopus 로고
    • Fractional Fourier optics
    • _, "Fractional Fourier optics." J. Opt. Soc. Am. A, vol. 12, pp 743-751, 1995.
    • (1995) J. Opt. Soc. Am. a , vol.12 , pp. 743-751
  • 21
    • 0028515765 scopus 로고
    • Fresnel diffraction and the fractional-order Fourie transform
    • P. Pellat-Finet, "Fresnel diffraction and the fractional-order Fourie transform," Opt. Lett., vol. 19, pp. 1388-1390, 1994.
    • (1994) Opt. Lett. , vol.19 , pp. 1388-1390
    • Pellat-Finet, P.1
  • 22
    • 0028494881 scopus 로고
    • Fractional-order F'ourier transform an Fourier optics
    • F. Pellat-Finet and G. Bonnet, "Fractional-order F'ourier transform an Fourier optics," Opt. Commun., vol. 111, pp. 141-154, 1994.
    • (1994) Opt. Commun. , vol.111 , pp. 141-154
    • Pellat-Finet, F.1    Bonnet, G.2
  • 23
    • 0028496555 scopus 로고
    • Fractional Fourier transforms an optical systems
    • L. M. Bernardo and O. D. D. Soares, "Fractional Fourier transforms an optical systems," Opt. Commun., vol. 110. pp. 517-522, 1994.
    • (1994) Opt. Commun. , vol.110 , pp. 517-522
    • Bernardo, L.M.1    Soares, O.D.D.2
  • 24
    • 33747740279 scopus 로고    scopus 로고
    • Fractional Fourier transforms and imaging
    • in print
    • _, "Fractional Fourier transforms and imaging," J. Opt. Soc. Am A, in print.
    • J. Opt. Soc. Am a
  • 28
    • 0028485528 scopus 로고
    • Tomographie time-frequency analysis and its application toward time-varying filtering and adaptive kernel design for multicomponent linear-FM signals
    • J. Wood and D. T. Barry, "Tomographie time-frequency analysis and its application toward time-varying filtering and adaptive kernel design for multicomponent linear-FM signals," IEEE Trans. Signal Processing, vol. 42, pp. 2094-2104, Aug. 1994 '
    • (1994) IEEE Trans. Signal Processing , vol.42 , pp. 2094-2104
    • Wood, J.1    Barry, D.T.2
  • 29
    • 0028483876 scopus 로고
    • Linear signal, synhesis using the Radon-Wigner transform
    • Aug.
    • _, "Linear signal, synhesis using the Radon-Wigner transform," IEEE Trans. Signal Processing, vol. 42, pp. 2105-2111, Aug. 1994
    • (1994) IEEE Trans. Signal Processing , vol.42 , pp. 2105-2111
  • 30
    • 0028539817 scopus 로고
    • Radun transformation of time-frequency distributions for analysis of multicomponent signals
    • Nov.
    • _, "Radun transformation of time-frequency distributions for analysis of multicomponent signals," 1ERE Trans. Signal Processing, vol. 42, pp. 3166-3177,Nov. 1994
    • (1994) 1ERE Trans. Signal Processing , vol.42 , pp. 3166-3177
  • 31
    • 0028459601 scopus 로고
    • Relationship between the RadonWigner and fractional Fourier transforms
    • A. W. Lohmann and B. H. Soffer, "Relationship between the RadonWigner and fractional Fourier transforms," J. Opt. Soc, Amer. A, vol. 11, pp. 1798-1801, 1994
    • (1994) J. Opt. Soc, Amer. A , vol.11 , pp. 1798-1801
    • Lohmann, A.W.1    Soffer, B.H.2
  • 32
    • 0028478769 scopus 로고
    • Fractional Fourier transforms, wavelet transforms, and adaptive neural networks
    • S.-Y. Lee and H. H. Szu, "Fractional Fourier transforms, wavelet transforms, and adaptive neural networks," Opt. Eng., vol. 33, pp. 2326-2330, 1994
    • (1994) Opt. Eng. , vol.33 , pp. 2326-2330
    • Lee, S.-Y.1    Szu, H.H.2
  • 33
    • 0026170450 scopus 로고
    • Adaptive chirplet representation of signals on time-frequency plane
    • D. Mihovilovic and R. N. Bracewell, "Adaptive chirplet representation of signals on time-frequency plane," Electron. Lett., vol. 27, pp. 1159-1161, 1991
    • (1991) Electron. Lett. , vol.27 , pp. 1159-1161
    • Mihovilovic, D.1    Bracewell, R.N.2
  • 34
    • 0001202611 scopus 로고
    • Whistler analysis in the time-frequency plane using chirplets
    • _, "Whistler analysis in the time-frequency plane using chirplets," J. Geophys. Res., vol. 97, pp. 17199-17204, 1992
    • (1992) J. Geophys. Res. , vol.97 , pp. 17199-17204
  • 35
    • 0026641896 scopus 로고
    • "Chirplets" and "warblets": Novel timefrequency methods
    • S. Mann and S. Haykin, ""Chirplets" and "warblets": novel timefrequency methods," Electron. Lett., vol. 28, pp. 114-116, 1992
    • (1992) Electron. Lett. , vol.28 , pp. 114-116
    • Mann, S.1    Haykin, S.2
  • 37
    • 85032751591 scopus 로고
    • Linear and quadratic timefrequency signal representations
    • Apr.
    • F. Hlawatsch and G. F. Bourdeaux-Bartels, "Linear and quadratic timefrequency signal representations," IEEE Signal Processing Mag., vol. 9, no. 2, pp. 21-67,Apr. 1992
    • (1992) IEEE Signal Processing Mag. , vol.9 , Issue.2 , pp. 21-67
    • Hlawatsch, F.1    Bourdeaux-Bartels, G.F.2
  • 38
    • 0024705330 scopus 로고
    • Time-frequency distributions-A review
    • L. Cohcn, "Time-frequency distributions-A review," Proc. IEEE, vol. 77, no. 7, pp. 941-981, My 1989
    • (1989) Proc. IEEE , vol.77 , Issue.7 , pp. 941-981
    • Cohcn, L.1
  • 40
    • 0019543409 scopus 로고
    • Interpolation and decimation of digital signals-A tutorial review
    • Mar.
    • R. E. Crochiere and L. R. Rabiner, "Interpolation and decimation of digital signals-A tutorial review," Proc. IEEE, vol. 69, no. 3, pp. 300-331,Mar. 1981
    • (1981) Proc. IEEE , vol.69 , Issue.3 , pp. 300-331
    • Crochiere, R.E.1    Rabiner, L.R.2
  • 41
    • 0020102107 scopus 로고
    • First-order optics-A canonical operator representation: Lossless systems J
    • M. Nazarathy and J. Shamir, "First-order optics-A canonical operator representation: Lossless systems," J. Opt. Soc., vol. 72, pp. 356-364, 1982
    • (1982) Opt. Soc. , vol.72 , pp. 356-364
    • Nazarathy, M.1    Shamir, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.