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Wigner-related phase spaces for signal processing and their optical implementation.

D Mendlovic1, Z Zalevsky, H M Ozaktas

  • 1Faculty of Engineering, Tel Aviv University, Israel. mend@eng.tau.ac.il

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 5, 2001
PubMed
Summary

This study introduces advanced Wigner-related phase spaces for enhanced signal processing, enabling better signal compression and recognition. Optical implementations of these generalized Wigner spaces and fractional Fourier transforms are demonstrated.

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Area of Science:

  • Signal processing
  • Optical physics
  • Mathematical physics

Background:

  • Phase spaces offer unique signal representations beneficial for compression and recognition.
  • Wigner-related representations have shown promise in improving signal processing capabilities.
  • Existing methods may have limitations in discrimination ability or implementation.

Purpose of the Study:

  • To present recently developed Wigner-related phase space representations.
  • To introduce and discuss optical implementations for these advanced representations.
  • To explore generalized Wigner spaces, fractional Fourier transform, and specific representations like x-p and r-p.

Main Methods:

  • Utilizing generalized Wigner spaces for signal representation.
  • Applying the fractional Fourier transform.

Related Experiment Videos

  • Investigating x-p and r-p representations.
  • Developing and demonstrating optical implementations.

    • Main Results:

    • Demonstrated improved signal processing performance using novel Wigner-related representations.
    • Successfully implemented optical systems for generalized Wigner spaces and fractional Fourier transform.
    • Showcased the practical application of x-p and r-p representations.

    Conclusions:

    • The presented Wigner-related phase spaces offer enhanced capabilities for signal processing tasks.
    • Optical implementations provide a viable pathway for realizing these advanced signal processing techniques.
    • Further exploration of generalized Wigner spaces and related transforms holds significant potential.