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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 3 — Mar. 1, 2004
  • pp: 360–366

Sampling in the light of Wigner distribution

Adrian Stern and Bahram Javidi  »View Author Affiliations


JOSA A, Vol. 21, Issue 3, pp. 360-366 (2004)
http://dx.doi.org/10.1364/JOSAA.21.000360


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Abstract

We propose a new method for analysis of the sampling and reconstruction conditions of real and complex signals by use of the Wigner domain. It is shown that the Wigner domain may provide a better understanding of the sampling process than the traditional Fourier domain. For example, it explains how certain nonbandlimited complex functions can be sampled and perfectly reconstructed. On the basis of observations in the Wigner domain, we derive a generalization to the Nyquist sampling criterion. By using this criterion, we demonstrate simple preprocessing operations that can adapt a signal that does not fulfill the Nyquist sampling criterion. The preprocessing operations demonstrated can be easily implemented by optical means.

© 2004 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(350.5500) Other areas of optics : Propagation
(350.6980) Other areas of optics : Transforms

Citation
Adrian Stern and Bahram Javidi, "Sampling in the light of Wigner distribution," J. Opt. Soc. Am. A 21, 360-366 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-3-360


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References

  1. C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 447–457 (1949).
  2. E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
  3. M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1980).
  4. G. Cristobal, C. Gonzalo, and J. Bescos, “Image filtering and analysis through the Wigner distribution,” in Advances in Electronics and Electron Physics Series, Vol. 80, P. W. Hawkes, ed. (Academic, Orlando, Fla., 1991), pp. 309–397.
  5. V. Arrizon and J. Ojeda-Castaneda, “Irradiance at Fresnel planes of a phase grating,” J. Opt. Soc. Am. A 9, 1801–1806 (1992).
  6. J. M. Whittaker, “The Fourier theory of the cardinal functions,” Proc.- R. Soc. Edinburgh Sect. A Math. 1, 169–176 (1929).
  7. A. Papoulis, “Pulse compression, fiber communication, and diffraction: a unified approach,” J. Opt. Soc. Am. A 11, 3–13 (1994).
  8. F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293–297 (1981).
  9. L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929–5935 (2000).
  10. A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. 43 (1), (2004).
  11. B. Boashash, Time–Frequency Analysis (Wiley, New York, 1992).
  12. A. V. Oppenheim and R. W. Schafer, Discrete Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  13. A. W. Lohmann, “Image rotation, Wigner distribution, and fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
  14. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
  15. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Understanding superesolution in Wigner space,” J. Opt. Soc. Am. A 17, 2422–2430 (2000).
  16. M. Unser, “Sampling—50 years after Shannon,” Proc. IEEE 88, 569–587 (2000).
  17. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  18. L. B. Almeida, “The fractional Fourier transform and time frequency representation,” IEEE Trans. Signal Process. 42, 3084–3091 (1994).
  19. D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, “Graded index fibers, Wigner distribution, and the fractal Fourier transform,” Appl. Opt. 33, 6188–6193 (1994).
  20. D. Dragoman, “Wigner-distribution-function representation of the coupling coefficient,” Appl. Opt. 34, 6758–6763 (1995).
  21. K. Grochenig, Foundation of Time–Frequency Analysis (Birkhäuser, Boston, Mass., 2001).

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