The Wigner Distribution - 1st Edition - ISBN: 9780444888563

The Wigner Distribution

1st Edition

Theory and Applications in Signal Processing

Editors: W. Mecklenbräuker Franz Hlawatsch
Hardcover ISBN: 9780444888563
Imprint: Elsevier Science
Published Date: 8th October 1997
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Institutional Access


Description

Positivity and Spread of Bilinear Time-Frequency Distributions
(A.J.E.M. Janssen).
Introduction. Cohen's class of bilinear time-frequency distributions. Time-frequency distributions and spread. Positivity properties of the Wigner distribution. Theorems of the Hudson type for Wigner-Rihaczek distributions. Wigner type theorems for bilinear time-frequency distributions. Smoothing bilinear time-frequency distributions. Some additional results and further developments. References.
The Interference Structure of the Wigner Distribution and Related Time-Frequency Signal Representations
(F. Hlawatsch, P. Flandrin).
Introduction.
Part I - Wigner Distribution
Outer interference. Interference geometry. Energetic interpretation of interference terms. Inner interference . The stationary-phase approximation. Singularities of interference terms. Sampling and aliasing.
Part II - Related Time-Frequency Representations. Generalized Wigner distribution. Ambiguity function. The shift-invariant class. The shift-scale-invariant class. Smoothed versions of Wigner distribution. Conclusion. References.
Signal Synthesis Algorithms for Bilinear Time-Frequency Signal Representations
(F. Hlawatsch, W. Krattenthaler)
Introduction. Subspace-unitary bilinear time-frequency representations. Wigner distribution. Smoothed versions of Wigner distribution. Spectrogram. On-line synthesis algorithms for pseudo Wigner distribution. Phase matching algorithms. Applications to time-frequency filtering. Conclusion. References.
The Wigner-Ville Spectrum of Nonstationary Random Signals
(P. Flandrin, W. Martin)
Introduction. Stationarity and nonstationarity. Definitions of time-dependent spectra. The Wigner-Ville spectrum. Estimation of the Wigner-Ville spectrum. Wigner-Ville based optimum detection. Conclusion. References.
Time-Varying Signal Processing Using Wigner Distribution Synthesis Techniques
(G.F. Boudreaux-Bartels)
Introduction. Time-varying signal processing applications of WD synthesis techniques. Cross Wigner distribution synthesis. Conclusions. Acknowledgements. References.
The Singular Value Decomposition of the Wigner Distribution and its Applications
(N.M. Marinovich)
Introduction. Outer product expansion of the Wigner distribution. Application to shape description and classification. Application to biomedical ultrasonic tissue characterization. Generalized SVD of the Wigner distribution - application to signal detection. Summary. References.
Application of the Wigner Distribution Function in Optics
(M.J. Bastiaans)
Introduction. Wigner distribution function as a local frequency spectrum. Examples of Wigner distribution functions. Properties of the Wigner distribution function. Ray spread function of an optical system. Transport equations for the Wigner distribution function. Wigner distribution function for partially coherent light. Applications of the Wigner distribution function in optics. Appendices. References. Bibliography for the years from 1985-1992. Subject index.

Table of Contents

Positivity and Spread of Bilinear Time-Frequency Distributions
(A.J.E.M. Janssen).
Introduction. Cohen's class of bilinear time-frequency distributions. Time-frequency distributions and spread. Positivity properties of the Wigner distribution. Theorems of the Hudson type for Wigner-Rihaczek distributions. Wigner type theorems for bilinear time-frequency distributions. Smoothing bilinear time-frequency distributions. Some additional results and further developments. References.
The Interference Structure of the Wigner Distribution and Related Time-Frequency Signal Representations
(F. Hlawatsch, P. Flandrin).
Introduction.
Part I - Wigner Distribution
Outer interference. Interference geometry. Energetic interpretation of interference terms. Inner interference . The stationary-phase approximation. Singularities of interference terms. Sampling and aliasing.
Part II - Related Time-Frequency Representations. Generalized Wigner distribution. Ambiguity function. The shift-invariant class. The shift-scale-invariant class. Smoothed versions of Wigner distribution. Conclusion. References.
Signal Synthesis Algorithms for Bilinear Time-Frequency Signal Representations
(F. Hlawatsch, W. Krattenthaler)
Introduction. Subspace-unitary bilinear time-frequency representations. Wigner distribution. Smoothed versions of Wigner distribution. Spectrogram. On-line synthesis algorithms for pseudo Wigner distribution. Phase matching algorithms. Applications to time-frequency filtering. Conclusion. References.
The Wigner-Ville Spectrum of Nonstationary Random Signals
(P. Flandrin, W. Martin)
Introduction. Stationarity and nonstationarity. Definitions of time-dependent spectra. The Wigner-Ville spectrum. Estimation of the Wigner-Ville spectrum. Wigner-Ville based optimum detection. Conclusion. References.
Time-Varying Signal Processing Using Wigner Distribution Synthesis Techniques
(G.F. Boudreaux-Bartels)
Introduction. Time-varying signal processing applications of WD synthesis techniques. Cross Wigner distribution synthesis. Conclusions. Acknowledgements. References.
The Singular Value Decomposition of the Wigner Distribution and its Applications
(N.M. Marinovich)
Introduction. Outer product expansion of the Wigner distribution. Application to shape description and classification. Application to biomedical ultrasonic tissue characterization. Generalized SVD of the Wigner distribution - application to signal detection. Summary. References.
Application of the Wigner Distribution Function in Optics
(M.J. Bastiaans)
Introduction. Wigner distribution function as a local frequency spectrum. Examples of Wigner distribution functions. Properties of the Wigner distribution function. Ray spread function of an optical system. Transport equations for the Wigner distribution function. Wigner distribution function for partially coherent light. Applications of the Wigner distribution function in optics. Appendices. References. Bibliography for the years from 1985-1992. Subject index.

Details

Language:
English
Copyright:
© Elsevier Science 1997
Published:
Imprint:
Elsevier Science
Hardcover ISBN:
9780444888563

About the Editor

W. Mecklenbräuker

Franz Hlawatsch

Affiliations and Expertise

Vienna University of Technology, Vienna, Austria

Reviews

"An invaluable source if you are involved with functions of both time and frequency, or of course of both space and spatial frequency" --Ultramicroscopy, Vol 75

"...an excellent overview of the theory and applications of the Wigner distribution in signal analysis...written by some of the leading researchers in this area..." --International Journal of Electronics & Communications

"...Thanks to its content, which has now become more or less classical material, this book should be a fine addition to the library of anyone interested in time-frequency signal analysis." --Mathematical Reviews