Abstract

Owing to the nonlinear nature of the problem, the transform orders in fractional Fourier-domain filtering configurations have usually not been optimized but chosen uniformly. We discuss the optimization of these orders for multi-channel-filtering configurations by first finding the optimal filter coefficients for a larger number of uniformly chosen orders, and then maintaining the most important ones. The method is illustrated with the problem of synthesizing desired mutual-intensity distributions. The method we propose allows those fractional Fourier domains, which add little benefit to the filtering process but increase the overall cost, to be pruned, so that comparable performance can be attained with less cost, or higher performance can be obtained with the same cost. The method we propose is more likely to be useful when confronted with low-cost rather than high-performance applications, because larger improvements are obtained when the use of a smaller number of filters is desired.

© 2002 Optical Society of America

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  1. L. B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans Signal Process. 42, 3084–3091 (1994).
    [CrossRef]
  2. O. Akay, G. F. Boudreaux-Bartels, “Unitary and Hermitian fractional operators and their relation to the fractional Fourier transform,” IEEE Signal Process. Lett. 5, 312–314 (1998).
    [CrossRef]
  3. T. Alieva, V. Lopez, F. Agullo-Lopez, L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
    [CrossRef]
  4. İ. Ş. Yetik, H. M. Ozaktas, B. Barshan, L. Onural, “Perspective projections in the space-frequency plane and fractional Fourier transforms,” J. Opt. Soc. Am. A 17, 2382–2390 (2000).
    [CrossRef]
  5. L. M. Bernardo, O. D. D. Soares, “Fractional Fourier transforms and imaging,” J. Opt. Soc. Am. A 11, 2622–2626 (1994).
    [CrossRef]
  6. W. X. Cong, N. X. Chen, B. Y. Gu, “Recursive algorithm for phase retrieval in the fractional Fourier transform domain,” Appl. Opt. 37, 6906–6910 (1998).
    [CrossRef]
  7. D. Dragoman, M. Dragoman, “Near and far field optical beam characterization using the fractional Fourier tansform,” Opt. Commun. 141, 5–9 (1997).
    [CrossRef]
  8. M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Propagation of mutual intensity expressed in terms of the fractional Fourier transform,” J. Opt. Soc. Am. A 13, 1068–1071 (1996).
    [CrossRef]
  9. M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Synthesis of mutual intensity distributions using the fractional Fourier transform,” Optics Commun. 125, 288–301 (1996).
    [CrossRef]
  10. J. García, R. G. Dorsch, A. W. Lohmann, C. Ferreira, Z. Zalevsky, “Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering,” Opt. Commun. 133, 393–400 (1997).
    [CrossRef]
  11. S. Granieri, R. Arizaga, E. E. Sicre, “Optical correlation based on the fractional Fourier transform,” Appl. Opt. 36, 6636–6645 (1997).
    [CrossRef]
  12. J. Hua, L. Liu, G. Li, “Scaled fractional Fourier transform and its optical implementation,” Appl. Opt. 36, 8490–8492 (1997).
    [CrossRef]
  13. C. J. Kuo, Y. Luo, “Generalized joint fractional Fourier transform correlators: a compact approach,” Appl. Opt. 37, 8270–8276 (1998).
    [CrossRef]
  14. S. Liu, J. Xu, Y. Zhang, L. Chen, C. Li, “General optical implementation of fractional Fourier transforms,” Opt. Lett. 20, 1053–1055 (1995).
    [CrossRef]
  15. A. W. Lohmann, Z. Zalevsky, D. Mendlovic, “Synthesis of pattern recognition filters for fractional Fourier processing,” Opt. Commun., 128, 199–204 (1996).
    [CrossRef]
  16. D. Mendlovic, Z. Zalevsky, H. M. Ozaktas, “Applications of the fractional Fourier transform to optical pattern recognition,” in Optical Pattern Recognition, (Cambridge University Press, Cambridge, 1998) Chap. 4, pp.89–125
  17. P. Pellat-Finet, “Fresnel diffraction and the fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994).
    [CrossRef] [PubMed]
  18. Z. Zalevsky, D. Medlovic, H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. Soc. A 2, 83–87 (2000).
    [CrossRef]
  19. Y. Zhang, B.-Y. Gu, “Rotation-invariant and controllable space-variant optical correlation,” Appl. Opt. 37, 6256–6261 (1998).
    [CrossRef]
  20. H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, (John Wiley & Sons, New York, 2001).
  21. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional order Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
    [CrossRef]
  22. A. W. Lohmann, B. H. Soffer, “Relationships between the Radon–Wigner and fractional Fourier transforms,” J. Opt. Soc. Am. A 11, 1798–1801 (1994).
    [CrossRef]
  23. D. Mustard, “The fractional Fourier transform and the Wigner distribution,” J Aust. Math. Soc. B 38, 209–219 (1996).
    [CrossRef]
  24. H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).
    [CrossRef]
  25. H. M. Ozaktas, B. Barshan, D. Mendlovic, “Convolution and filtering in fractional Fourier domains,” Opt. Rev. 1, 15–16 (1994).
    [CrossRef]
  26. Ç. Candan, M. A. Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).
    [CrossRef]
  27. M. A. Kutay, H. M. Ozaktas, O. Arikan, L. Onural, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
    [CrossRef]
  28. Z. Zalevsky, D. Mendlovic, “Fractional Wiener filter,” Appl. Opt. 35, 3930–3936 (1996).
    [CrossRef] [PubMed]
  29. M. F. Erden, M. A. Kutay, H. M. Ozaktas, “Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration,” IEEE Trans. Signal Process. 47, 1458–1462 (1999).
    [CrossRef]
  30. M. F. Erden, H. M. Ozaktas, “Synthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains,” J. Opt. Soc. Am. A 15, 1647–1657 (1998).
    [CrossRef]
  31. M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ö Güleryüz, Ç. Candan, “Space-bandwidth-efficient realizations of linear systems,” Opt. Lett. 23, 1069–1071 (1998).
    [CrossRef]
  32. M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ç. Candan, Ö Güleryüz, “Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Process. (IEEE, Piscataway, N. J., 1998) pp. 3433–3436.
  33. M. A. Kutay, H. Özaktaş, M. F. Erden, H. M. Ozaktas, O. Arikan, “Solution and cost analysis of general multi-channel and multi-stage filtering circuits,” in Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (IEEE, Piscataway, N. J., 1998) pp. 481–484.
  34. M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).
    [CrossRef]
  35. İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition, ”in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (IEEE, Piscataway, N. J., 2000) Vol. I, pp. 93–96.
  36. H. M. Ozaktas, M. A. Kutay, D. Mendlovic, “Introduction to the fractional Fourier transform and its applications” in P. W. Hawkes, ed., Advances in Imaging and Electron Physics, Vol. 106 (Academic Press, San Diego, Calif., 1999) Chap. 4, pp. 239–291.
  37. D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I, J. Opt. Soc. Am. A 10, 1875–1881 (1993).
    [CrossRef]
  38. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II.” J. Opt. Soc. Am. A 10, 2522–2531 (1993).
    [CrossRef]
  39. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995).
    [CrossRef]
  40. B. Barshan, M. A. Kutay, H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32–36 (1997).
    [CrossRef]

2000 (3)

Z. Zalevsky, D. Medlovic, H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. Soc. A 2, 83–87 (2000).
[CrossRef]

Ç. Candan, M. A. Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).
[CrossRef]

İ. Ş. Yetik, H. M. Ozaktas, B. Barshan, L. Onural, “Perspective projections in the space-frequency plane and fractional Fourier transforms,” J. Opt. Soc. Am. A 17, 2382–2390 (2000).
[CrossRef]

1999 (2)

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).
[CrossRef]

M. F. Erden, M. A. Kutay, H. M. Ozaktas, “Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration,” IEEE Trans. Signal Process. 47, 1458–1462 (1999).
[CrossRef]

1998 (6)

1997 (6)

S. Granieri, R. Arizaga, E. E. Sicre, “Optical correlation based on the fractional Fourier transform,” Appl. Opt. 36, 6636–6645 (1997).
[CrossRef]

J. Hua, L. Liu, G. Li, “Scaled fractional Fourier transform and its optical implementation,” Appl. Opt. 36, 8490–8492 (1997).
[CrossRef]

M. A. Kutay, H. M. Ozaktas, O. Arikan, L. Onural, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
[CrossRef]

D. Dragoman, M. Dragoman, “Near and far field optical beam characterization using the fractional Fourier tansform,” Opt. Commun. 141, 5–9 (1997).
[CrossRef]

J. García, R. G. Dorsch, A. W. Lohmann, C. Ferreira, Z. Zalevsky, “Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering,” Opt. Commun. 133, 393–400 (1997).
[CrossRef]

B. Barshan, M. A. Kutay, H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32–36 (1997).
[CrossRef]

1996 (5)

A. W. Lohmann, Z. Zalevsky, D. Mendlovic, “Synthesis of pattern recognition filters for fractional Fourier processing,” Opt. Commun., 128, 199–204 (1996).
[CrossRef]

D. Mustard, “The fractional Fourier transform and the Wigner distribution,” J Aust. Math. Soc. B 38, 209–219 (1996).
[CrossRef]

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Synthesis of mutual intensity distributions using the fractional Fourier transform,” Optics Commun. 125, 288–301 (1996).
[CrossRef]

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Propagation of mutual intensity expressed in terms of the fractional Fourier transform,” J. Opt. Soc. Am. A 13, 1068–1071 (1996).
[CrossRef]

Z. Zalevsky, D. Mendlovic, “Fractional Wiener filter,” Appl. Opt. 35, 3930–3936 (1996).
[CrossRef] [PubMed]

1995 (2)

1994 (7)

1993 (3)

Agullo-Lopez, F.

T. Alieva, V. Lopez, F. Agullo-Lopez, L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
[CrossRef]

Akay, O.

O. Akay, G. F. Boudreaux-Bartels, “Unitary and Hermitian fractional operators and their relation to the fractional Fourier transform,” IEEE Signal Process. Lett. 5, 312–314 (1998).
[CrossRef]

Alieva, T.

T. Alieva, V. Lopez, F. Agullo-Lopez, L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
[CrossRef]

Almeida, L. B.

T. Alieva, V. Lopez, F. Agullo-Lopez, L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
[CrossRef]

L. B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans Signal Process. 42, 3084–3091 (1994).
[CrossRef]

Arikan, O.

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).
[CrossRef]

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ö Güleryüz, Ç. Candan, “Space-bandwidth-efficient realizations of linear systems,” Opt. Lett. 23, 1069–1071 (1998).
[CrossRef]

M. A. Kutay, H. M. Ozaktas, O. Arikan, L. Onural, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
[CrossRef]

M. A. Kutay, H. Özaktaş, M. F. Erden, H. M. Ozaktas, O. Arikan, “Solution and cost analysis of general multi-channel and multi-stage filtering circuits,” in Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (IEEE, Piscataway, N. J., 1998) pp. 481–484.

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ç. Candan, Ö Güleryüz, “Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Process. (IEEE, Piscataway, N. J., 1998) pp. 3433–3436.

Arizaga, R.

Barshan, B.

Bernardo, L. M.

Boudreaux-Bartels, G. F.

O. Akay, G. F. Boudreaux-Bartels, “Unitary and Hermitian fractional operators and their relation to the fractional Fourier transform,” IEEE Signal Process. Lett. 5, 312–314 (1998).
[CrossRef]

Candan, Ç.

Ç. Candan, M. A. Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).
[CrossRef]

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ö Güleryüz, Ç. Candan, “Space-bandwidth-efficient realizations of linear systems,” Opt. Lett. 23, 1069–1071 (1998).
[CrossRef]

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ç. Candan, Ö Güleryüz, “Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Process. (IEEE, Piscataway, N. J., 1998) pp. 3433–3436.

Chen, L.

Chen, N. X.

Cong, W. X.

Dorsch, R. G.

J. García, R. G. Dorsch, A. W. Lohmann, C. Ferreira, Z. Zalevsky, “Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering,” Opt. Commun. 133, 393–400 (1997).
[CrossRef]

Dragoman, D.

D. Dragoman, M. Dragoman, “Near and far field optical beam characterization using the fractional Fourier tansform,” Opt. Commun. 141, 5–9 (1997).
[CrossRef]

Dragoman, M.

D. Dragoman, M. Dragoman, “Near and far field optical beam characterization using the fractional Fourier tansform,” Opt. Commun. 141, 5–9 (1997).
[CrossRef]

Erden, M. F.

M. F. Erden, M. A. Kutay, H. M. Ozaktas, “Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration,” IEEE Trans. Signal Process. 47, 1458–1462 (1999).
[CrossRef]

M. F. Erden, H. M. Ozaktas, “Synthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains,” J. Opt. Soc. Am. A 15, 1647–1657 (1998).
[CrossRef]

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ö Güleryüz, Ç. Candan, “Space-bandwidth-efficient realizations of linear systems,” Opt. Lett. 23, 1069–1071 (1998).
[CrossRef]

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Propagation of mutual intensity expressed in terms of the fractional Fourier transform,” J. Opt. Soc. Am. A 13, 1068–1071 (1996).
[CrossRef]

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Synthesis of mutual intensity distributions using the fractional Fourier transform,” Optics Commun. 125, 288–301 (1996).
[CrossRef]

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ç. Candan, Ö Güleryüz, “Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Process. (IEEE, Piscataway, N. J., 1998) pp. 3433–3436.

M. A. Kutay, H. Özaktaş, M. F. Erden, H. M. Ozaktas, O. Arikan, “Solution and cost analysis of general multi-channel and multi-stage filtering circuits,” in Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (IEEE, Piscataway, N. J., 1998) pp. 481–484.

Ferreira, C.

J. García, R. G. Dorsch, A. W. Lohmann, C. Ferreira, Z. Zalevsky, “Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering,” Opt. Commun. 133, 393–400 (1997).
[CrossRef]

García, J.

J. García, R. G. Dorsch, A. W. Lohmann, C. Ferreira, Z. Zalevsky, “Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering,” Opt. Commun. 133, 393–400 (1997).
[CrossRef]

Granieri, S.

Gu, B. Y.

Gu, B.-Y.

Güleryüz, Ö

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ö Güleryüz, Ç. Candan, “Space-bandwidth-efficient realizations of linear systems,” Opt. Lett. 23, 1069–1071 (1998).
[CrossRef]

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ç. Candan, Ö Güleryüz, “Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Process. (IEEE, Piscataway, N. J., 1998) pp. 3433–3436.

Hua, J.

Kuo, C. J.

Kutay, M. A.

Ç. Candan, M. A. Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).
[CrossRef]

M. F. Erden, M. A. Kutay, H. M. Ozaktas, “Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration,” IEEE Trans. Signal Process. 47, 1458–1462 (1999).
[CrossRef]

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).
[CrossRef]

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ö Güleryüz, Ç. Candan, “Space-bandwidth-efficient realizations of linear systems,” Opt. Lett. 23, 1069–1071 (1998).
[CrossRef]

M. A. Kutay, H. M. Ozaktas, O. Arikan, L. Onural, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
[CrossRef]

B. Barshan, M. A. Kutay, H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32–36 (1997).
[CrossRef]

M. A. Kutay, H. Özaktaş, M. F. Erden, H. M. Ozaktas, O. Arikan, “Solution and cost analysis of general multi-channel and multi-stage filtering circuits,” in Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (IEEE, Piscataway, N. J., 1998) pp. 481–484.

H. M. Ozaktas, M. A. Kutay, D. Mendlovic, “Introduction to the fractional Fourier transform and its applications” in P. W. Hawkes, ed., Advances in Imaging and Electron Physics, Vol. 106 (Academic Press, San Diego, Calif., 1999) Chap. 4, pp. 239–291.

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ç. Candan, Ö Güleryüz, “Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Process. (IEEE, Piscataway, N. J., 1998) pp. 3433–3436.

H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, (John Wiley & Sons, New York, 2001).

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition, ”in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (IEEE, Piscataway, N. J., 2000) Vol. I, pp. 93–96.

Li, C.

Li, G.

Liu, L.

Liu, S.

Lohmann, A. W.

J. García, R. G. Dorsch, A. W. Lohmann, C. Ferreira, Z. Zalevsky, “Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering,” Opt. Commun. 133, 393–400 (1997).
[CrossRef]

A. W. Lohmann, Z. Zalevsky, D. Mendlovic, “Synthesis of pattern recognition filters for fractional Fourier processing,” Opt. Commun., 128, 199–204 (1996).
[CrossRef]

A. W. Lohmann, B. H. Soffer, “Relationships between the Radon–Wigner and fractional Fourier transforms,” J. Opt. Soc. Am. A 11, 1798–1801 (1994).
[CrossRef]

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional order Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
[CrossRef]

Lopez, V.

T. Alieva, V. Lopez, F. Agullo-Lopez, L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
[CrossRef]

Luo, Y.

M. Ozaktas, H.

Ç. Candan, M. A. Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).
[CrossRef]

Medlovic, D.

Z. Zalevsky, D. Medlovic, H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. Soc. A 2, 83–87 (2000).
[CrossRef]

Mendlovic, D.

A. W. Lohmann, Z. Zalevsky, D. Mendlovic, “Synthesis of pattern recognition filters for fractional Fourier processing,” Opt. Commun., 128, 199–204 (1996).
[CrossRef]

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Synthesis of mutual intensity distributions using the fractional Fourier transform,” Optics Commun. 125, 288–301 (1996).
[CrossRef]

Z. Zalevsky, D. Mendlovic, “Fractional Wiener filter,” Appl. Opt. 35, 3930–3936 (1996).
[CrossRef] [PubMed]

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Propagation of mutual intensity expressed in terms of the fractional Fourier transform,” J. Opt. Soc. Am. A 13, 1068–1071 (1996).
[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995).
[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, “Convolution and filtering in fractional Fourier domains,” Opt. Rev. 1, 15–16 (1994).
[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).
[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II.” J. Opt. Soc. Am. A 10, 2522–2531 (1993).
[CrossRef]

D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I, J. Opt. Soc. Am. A 10, 1875–1881 (1993).
[CrossRef]

H. M. Ozaktas, M. A. Kutay, D. Mendlovic, “Introduction to the fractional Fourier transform and its applications” in P. W. Hawkes, ed., Advances in Imaging and Electron Physics, Vol. 106 (Academic Press, San Diego, Calif., 1999) Chap. 4, pp. 239–291.

D. Mendlovic, Z. Zalevsky, H. M. Ozaktas, “Applications of the fractional Fourier transform to optical pattern recognition,” in Optical Pattern Recognition, (Cambridge University Press, Cambridge, 1998) Chap. 4, pp.89–125

Mustard, D.

D. Mustard, “The fractional Fourier transform and the Wigner distribution,” J Aust. Math. Soc. B 38, 209–219 (1996).
[CrossRef]

Onural, L.

Ozaktas, H. M.

İ. Ş. Yetik, H. M. Ozaktas, B. Barshan, L. Onural, “Perspective projections in the space-frequency plane and fractional Fourier transforms,” J. Opt. Soc. Am. A 17, 2382–2390 (2000).
[CrossRef]

Z. Zalevsky, D. Medlovic, H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. Soc. A 2, 83–87 (2000).
[CrossRef]

M. F. Erden, M. A. Kutay, H. M. Ozaktas, “Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration,” IEEE Trans. Signal Process. 47, 1458–1462 (1999).
[CrossRef]

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).
[CrossRef]

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ö Güleryüz, Ç. Candan, “Space-bandwidth-efficient realizations of linear systems,” Opt. Lett. 23, 1069–1071 (1998).
[CrossRef]

M. F. Erden, H. M. Ozaktas, “Synthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains,” J. Opt. Soc. Am. A 15, 1647–1657 (1998).
[CrossRef]

B. Barshan, M. A. Kutay, H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32–36 (1997).
[CrossRef]

M. A. Kutay, H. M. Ozaktas, O. Arikan, L. Onural, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
[CrossRef]

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Propagation of mutual intensity expressed in terms of the fractional Fourier transform,” J. Opt. Soc. Am. A 13, 1068–1071 (1996).
[CrossRef]

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Synthesis of mutual intensity distributions using the fractional Fourier transform,” Optics Commun. 125, 288–301 (1996).
[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995).
[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, “Convolution and filtering in fractional Fourier domains,” Opt. Rev. 1, 15–16 (1994).
[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).
[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II.” J. Opt. Soc. Am. A 10, 2522–2531 (1993).
[CrossRef]

D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I, J. Opt. Soc. Am. A 10, 1875–1881 (1993).
[CrossRef]

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ç. Candan, Ö Güleryüz, “Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Process. (IEEE, Piscataway, N. J., 1998) pp. 3433–3436.

M. A. Kutay, H. Özaktaş, M. F. Erden, H. M. Ozaktas, O. Arikan, “Solution and cost analysis of general multi-channel and multi-stage filtering circuits,” in Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (IEEE, Piscataway, N. J., 1998) pp. 481–484.

H. M. Ozaktas, M. A. Kutay, D. Mendlovic, “Introduction to the fractional Fourier transform and its applications” in P. W. Hawkes, ed., Advances in Imaging and Electron Physics, Vol. 106 (Academic Press, San Diego, Calif., 1999) Chap. 4, pp. 239–291.

H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, (John Wiley & Sons, New York, 2001).

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition, ”in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (IEEE, Piscataway, N. J., 2000) Vol. I, pp. 93–96.

D. Mendlovic, Z. Zalevsky, H. M. Ozaktas, “Applications of the fractional Fourier transform to optical pattern recognition,” in Optical Pattern Recognition, (Cambridge University Press, Cambridge, 1998) Chap. 4, pp.89–125

Özaktas, H.

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).
[CrossRef]

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition, ”in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (IEEE, Piscataway, N. J., 2000) Vol. I, pp. 93–96.

M. A. Kutay, H. Özaktaş, M. F. Erden, H. M. Ozaktas, O. Arikan, “Solution and cost analysis of general multi-channel and multi-stage filtering circuits,” in Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (IEEE, Piscataway, N. J., 1998) pp. 481–484.

Pellat-Finet, P.

Sicre, E. E.

Soares, O. D. D.

Soffer, B. H.

Xu, J.

Yetik, I. S.

İ. Ş. Yetik, H. M. Ozaktas, B. Barshan, L. Onural, “Perspective projections in the space-frequency plane and fractional Fourier transforms,” J. Opt. Soc. Am. A 17, 2382–2390 (2000).
[CrossRef]

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition, ”in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (IEEE, Piscataway, N. J., 2000) Vol. I, pp. 93–96.

Zalevsky, Z.

Z. Zalevsky, D. Medlovic, H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. Soc. A 2, 83–87 (2000).
[CrossRef]

J. García, R. G. Dorsch, A. W. Lohmann, C. Ferreira, Z. Zalevsky, “Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering,” Opt. Commun. 133, 393–400 (1997).
[CrossRef]

A. W. Lohmann, Z. Zalevsky, D. Mendlovic, “Synthesis of pattern recognition filters for fractional Fourier processing,” Opt. Commun., 128, 199–204 (1996).
[CrossRef]

Z. Zalevsky, D. Mendlovic, “Fractional Wiener filter,” Appl. Opt. 35, 3930–3936 (1996).
[CrossRef] [PubMed]

D. Mendlovic, Z. Zalevsky, H. M. Ozaktas, “Applications of the fractional Fourier transform to optical pattern recognition,” in Optical Pattern Recognition, (Cambridge University Press, Cambridge, 1998) Chap. 4, pp.89–125

H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, (John Wiley & Sons, New York, 2001).

Zhang, Y.

Appl. Opt. (6)

IEEE Signal Process. Lett. (1)

O. Akay, G. F. Boudreaux-Bartels, “Unitary and Hermitian fractional operators and their relation to the fractional Fourier transform,” IEEE Signal Process. Lett. 5, 312–314 (1998).
[CrossRef]

IEEE Trans Signal Process. (1)

L. B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans Signal Process. 42, 3084–3091 (1994).
[CrossRef]

IEEE Trans. Signal Process. (3)

Ç. Candan, M. A. Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).
[CrossRef]

M. A. Kutay, H. M. Ozaktas, O. Arikan, L. Onural, “Optimal filtering in fractional Fourier domains,” IEEE Trans. Signal Process. 45, 1129–1143 (1997).
[CrossRef]

M. F. Erden, M. A. Kutay, H. M. Ozaktas, “Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration,” IEEE Trans. Signal Process. 47, 1458–1462 (1999).
[CrossRef]

J Aust. Math. Soc. B (1)

D. Mustard, “The fractional Fourier transform and the Wigner distribution,” J Aust. Math. Soc. B 38, 209–219 (1996).
[CrossRef]

J. Mod. Opt. (1)

T. Alieva, V. Lopez, F. Agullo-Lopez, L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
[CrossRef]

J. Opt. Soc. A (1)

Z. Zalevsky, D. Medlovic, H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. Soc. A 2, 83–87 (2000).
[CrossRef]

J. Opt. Soc. Am. A (10)

İ. Ş. Yetik, H. M. Ozaktas, B. Barshan, L. Onural, “Perspective projections in the space-frequency plane and fractional Fourier transforms,” J. Opt. Soc. Am. A 17, 2382–2390 (2000).
[CrossRef]

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Propagation of mutual intensity expressed in terms of the fractional Fourier transform,” J. Opt. Soc. Am. A 13, 1068–1071 (1996).
[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995).
[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).
[CrossRef]

A. W. Lohmann, B. H. Soffer, “Relationships between the Radon–Wigner and fractional Fourier transforms,” J. Opt. Soc. Am. A 11, 1798–1801 (1994).
[CrossRef]

L. M. Bernardo, O. D. D. Soares, “Fractional Fourier transforms and imaging,” J. Opt. Soc. Am. A 11, 2622–2626 (1994).
[CrossRef]

M. F. Erden, H. M. Ozaktas, “Synthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains,” J. Opt. Soc. Am. A 15, 1647–1657 (1998).
[CrossRef]

D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I, J. Opt. Soc. Am. A 10, 1875–1881 (1993).
[CrossRef]

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional order Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II.” J. Opt. Soc. Am. A 10, 2522–2531 (1993).
[CrossRef]

Opt. Commun. (4)

J. García, R. G. Dorsch, A. W. Lohmann, C. Ferreira, Z. Zalevsky, “Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering,” Opt. Commun. 133, 393–400 (1997).
[CrossRef]

A. W. Lohmann, Z. Zalevsky, D. Mendlovic, “Synthesis of pattern recognition filters for fractional Fourier processing,” Opt. Commun., 128, 199–204 (1996).
[CrossRef]

D. Dragoman, M. Dragoman, “Near and far field optical beam characterization using the fractional Fourier tansform,” Opt. Commun. 141, 5–9 (1997).
[CrossRef]

B. Barshan, M. A. Kutay, H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32–36 (1997).
[CrossRef]

Opt. Lett. (3)

Opt. Rev. (1)

H. M. Ozaktas, B. Barshan, D. Mendlovic, “Convolution and filtering in fractional Fourier domains,” Opt. Rev. 1, 15–16 (1994).
[CrossRef]

Optics Commun. (1)

M. F. Erden, H. M. Ozaktas, D. Mendlovic, “Synthesis of mutual intensity distributions using the fractional Fourier transform,” Optics Commun. 125, 288–301 (1996).
[CrossRef]

Signal Process. (1)

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).
[CrossRef]

Other (6)

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition, ”in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (IEEE, Piscataway, N. J., 2000) Vol. I, pp. 93–96.

H. M. Ozaktas, M. A. Kutay, D. Mendlovic, “Introduction to the fractional Fourier transform and its applications” in P. W. Hawkes, ed., Advances in Imaging and Electron Physics, Vol. 106 (Academic Press, San Diego, Calif., 1999) Chap. 4, pp. 239–291.

M. A. Kutay, M. F. Erden, H. M. Ozaktas, O. Arikan, Ç. Candan, Ö Güleryüz, “Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Process. (IEEE, Piscataway, N. J., 1998) pp. 3433–3436.

M. A. Kutay, H. Özaktaş, M. F. Erden, H. M. Ozaktas, O. Arikan, “Solution and cost analysis of general multi-channel and multi-stage filtering circuits,” in Proceedings of the 1998 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (IEEE, Piscataway, N. J., 1998) pp. 481–484.

D. Mendlovic, Z. Zalevsky, H. M. Ozaktas, “Applications of the fractional Fourier transform to optical pattern recognition,” in Optical Pattern Recognition, (Cambridge University Press, Cambridge, 1998) Chap. 4, pp.89–125

H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, (John Wiley & Sons, New York, 2001).

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