Publication: Importance of the phase and amplitude in the fractional Fourier domain
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2003-03
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Alieva, Tatiana Krasheninnikova
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Optical Society of America
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Abstract
The importance of the amplitude and phase in the fractional Fourier transform (FT) domain is analyzed on the basis of the rectangular signal and the real-world image. The quality of signal restoration from only the amplitude or from only the phase of its fractional FT by applying the inverse fractional FT is considered. It is shown that the signal reconstructed from the amplitude of the fractional FT usually reveals the main features of the original signal only for relatively low fractional orders. On the basis of phase information in the fractional FT domains, significant details of the signal can be obtained for nearly all fractional orders.
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© 2003 Optical Society of America.
Financial assistance from the Spanish Ministry of Science and Technology (project TIC 2002-01846) is acknowledged. T. Alieva acknowledges the financial support of Secretaría de Estado de Educación y Universidades de España (SB2000-0166) (Spanish Ministry of Education, Culture, and Sports).
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1. J. L. Horner and P. D. Gianino, “Phase-only matched filtering”, Appl. Opt. 23, 812–816 (1984).
2. A. Vanderlugt, Optical Signal Processing (Wiley, New York, 1992).
3. G. O. Reynolds, J. B. DeVelis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE Press, Bellingham, Wash., 1989).
4. D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, “Fractional correlation”, Appl. Opt. 34, 303–309 (1995).
5. D. Mendlovic, Y. Bitran, R. G. Dorsch, and A. Lohmann, “Optical fractional correlation: experimental results”, J. Opt. Soc. Am. A 12, 1665–1670 (1995).
6. J. García, D. Mendlovic, Z. Zalevsky, and A. Lohmann, “Space variant simultaneous detection of several objects using multiple anamorphic fractional Fourier transform filters”, Appl. Opt. 35, 3945–3952 (1996).
7. J. Garcia, R. G. Dorsch, A. W. Lohmann, C. Ferreira, and Z. Zalevsky, “Flexible optical implementation of fractional Fourier processors: application to correlation and filtering”, Opt. Commun. 133, 393–400 (1997).
8. O. Akay and G. F. Boudreaux-Bartels, “Fractional convolution and correlation via operator methods and an application to detection of linear FM signals”, IEEE Trans. Signal Process. 49, 979–993 (2001).
9. T. Alieva and M. L. Calvo, “Generalized fractional convolution”, in Perspectives in Modern Optics and Optical Instrumentation (Anita Publications, New Delhi, 2002), pp. 282–292.
10. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, New York, 2001).
11. A. Kozma and D. Kelly, “Spatial filtering for detection of signals submerged in noise”, Appl. Opt. 4, 387–392 (1965).
12. A. V. Oppenheim and J. S. Lim, “The importance of phase in signals”, Proc. IEEE 69, 529–541 (1981).
13. L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device”, IBM J. Res. Dev. 13, 150–155 (1969).
14. A. W. Lohmann, D. Mendlovic, and G. Shabtay, “Significance of phase and amplitude in the Fourier domain”, J. Opt. Soc. Am. A 14, 2901–2904 (1997).
15. D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I”, J. Opt. Soc. Am. A 10, 1875–1881 (1993).
16. H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transformations and their optical implementation: II”, J. Opt. Soc. Am. A 10, 2522–2531 (1993).
17. L. B. Almeida, “The fractional Fourier transform and time-frequency representations”, IEEE Trans. Signal Process. 42, 3084–3091 (1994).
18. T. Alieva, M. L. Calvo, and M. J. Bastiaans, “Power filtering of n-order in the fractional Fourier domain”, J. Phys. A 35, 7779–7785 (2002).
19. M. Abramovich and I. A. Segun, Handbook of Mathematical Functions (Dover, New York, 1965).
20. H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, “Digital computation of the fractional Fourier transform”, IEEE Trans. Signal Process. 44, 2141–2150 (1996).