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Applied Optics

Applied Optics


  • Vol. 37, Iss. 11 — Apr. 10, 1998
  • pp: 2142–2144

Proposal for optical implementation of the Wigner distribution function

Gal Shabtay, David Mendlovic, and Zeev Zalevsky  »View Author Affiliations

Applied Optics, Vol. 37, Issue 11, pp. 2142-2144 (1998)

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The Wigner distribution function (WDF) offers comprehensive insight into a signal, for it employs both space (or time) and frequency simultaneously. Whenever optical signals are involved, the importance of the WDF is significantly higher because of the diffraction (or dispersion) behavior of optical signals. Novel optical implementations of the WDF and of the inverse Wigner transform are proposed. Both implementations are based on bulk optics elements incorporating joint transform correlator architecture. A similar implementation is derived for the ambiguity function, which is related to the WDF through Fourier transformation.

© 1998 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
(070.4790) Fourier optics and signal processing : Spectrum analysis
(070.6020) Fourier optics and signal processing : Continuous optical signal processing

Original Manuscript: September 2, 1997
Revised Manuscript: December 17, 1997
Published: April 10, 1998

Gal Shabtay, David Mendlovic, and Zeev Zalevsky, "Proposal for optical implementation of the Wigner distribution function," Appl. Opt. 37, 2142-2144 (1998)

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  1. J. C. Wood, D. T. Barry, “Tomographic time–frequency analysis and its application toward time-varying filtering and adaptive kernel design for multicomponent linear-FM signals,” IEEE Trans. Signal Process. 42, 2094–2103 (1994). [CrossRef]
  2. F. Hlawatsch, G. F. Boudreaux-Bartels, “Linear and quadratic time–frequency signal representations,” IEEE Signal Process. Mag. 9(2), 21–67 (1992). [CrossRef]
  3. M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978). [CrossRef]
  4. K. H. Brenner, A. W. Lohmann, “Wigner distribution function display of complex 1-D signals,” Opt. Commun. 42, 310–314 (1982). [CrossRef]
  5. H. Weber, “Wave optical analysis of the phase space analyser,” J. Mod. Opt. 39, 543–559 (1992). [CrossRef]
  6. D. Dragoman, M. Dragoman, “Wigner-transform implementation in the time-frequency domain,” Appl. Opt. 35, 7025–7030 (1996). [CrossRef] [PubMed]
  7. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1250 (1966). [CrossRef] [PubMed]

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