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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 20 — Jul. 10, 2002
  • pp: 4078–4084

Optimization of orders in multichannel fractional Fourier-domain filtering circuits and its application to the synthesis of mutual-intensity distributions

İmam Şamil Yetik, Mehmet Alper Kutay, and Haldun Memduh Ozaktas  »View Author Affiliations


Applied Optics, Vol. 41, Issue 20, pp. 4078-4084 (2002)
http://dx.doi.org/10.1364/AO.41.004078


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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

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms

History
Original Manuscript: March 6, 2001
Revised Manuscript: January 11, 2002
Published: July 10, 2002

Citation
İmam Şamil Yetik, Mehmet Alper Kutay, and Haldun Memduh Ozaktas, "Optimization of orders in multichannel fractional Fourier-domain filtering circuits and its application to the synthesis of mutual-intensity distributions," Appl. Opt. 41, 4078-4084 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-20-4078


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References

  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]

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