Processing of Non-Stationary Vibrations Using the Affine Wigner Distribution

  • Marcelo Iribarren
  • Cesar San Martin
  • Pedro Saavedra
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


This paper deals with the processing of non-stationary signals applied to rotating-machines condition monitoring. The advantages of applying the affine Wigner distribution is explored. First a brief synthesis of this technique and other related time-frequency distributions is given to exhibit their advantages, in particular when faults to diagnose are characterized by complex changes in spectrum or by weak non-stationarities in the vibration signal. Testing on synthesized and real signals shows it as a promising tool when compared to the Wavelet transform or smoothed pseudo Wigner-Ville distribution.


Attenuation Covariance Radar Expense Convolution 


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  1. [1]
    J. Bertrand and P. Bertrand. Affine Time-Frequency Distributions. In Time-Frequency Signal Analysis. Edited by B. Boashash, Longman Cheschire Pub., 1992.Google Scholar
  2. [2]
    R. G. Barianuk and D. L. Jones. A Signal-dependent Time-frequency Representation: Fast Algorithm for Optimal Kernel Design. IEEE Trans. on ASSP, 42(1):134–146, 1994.CrossRefGoogle Scholar
  3. [3]
    L. Cohen. A Primer on Time-Frequency Analysis. In Time-Frequency Signal Analysis. Edited by B. Boashash, Longman Cheschire Pub., 1992.Google Scholar
  4. [4]
    W. Choi and W. J. Williams. Improved Time-Frequency Representation of Multicomponent signals using Exponential Kernels. IEEE Trans. on ASSP, 37(6):862–871, 1989.CrossRefGoogle Scholar
  5. [5]
    P. Gonçalvès and R. G. Barianuk. Pseudo Affine Wigner Distributions: Definition and Kernel Formulation. Submitted to IEEE Trans. on Signal Processing, EDICS No. SP-2.3.1., 1996.Google Scholar
  6. [6]
    Ch. Heitz. Optimum Time-Frequency Representations for the Classification and Detection of Signals. Applied Sig. Process., 2(3):124–143, 1995.Google Scholar
  7. [7]
    F. Hlawatsch and G. F. Boudreaux-Bartels. Linear and Quadratic Time-Frequency Signal Representations. IEEE Signal Processing Magazine, 21-67, 1053-5888/92, 1992.Google Scholar
  8. [8]
    F. Hlawatsch and P. Flandrin. The Interference Structure of the Wigner Distribution and Related Time-Frequency Signal Representations. In The Wigner Distribution — Theory and Applications in Signal Processing. Edited by W. Mecklenbräuker, Elsevier, Amsterdam, 1995.Google Scholar
  9. [9]
    M. Iribarren et al. Perspectives of Time-Frequency Distributions to the Analysis of Rotating Machinery Vibrations, In Proc. IX Conference on Numerical Methods and its Applications, Bariloche, Argentina (in Spanish), 1995.Google Scholar
  10. [10]
    M. Iribarren, I. Foppiano, and P. Saavedra. Contributions of new Time-Frequency Distributions to Non Stationary Signal Detection, In Proc. XII Chilean Conference on Automatic Control, pp. 279-286, Santiago de Chile, 1996.Google Scholar
  11. [11]
    M. Iribarren, E. Zabala, and P. Saavedra. Wavelet Signal Processing of Nonstationary Vibrations for Machinery Condition Monitoring (in Spanish), In Proc. 7th. Latin-American Conference on Automatic Control, pp. 803–809, Buenos Aires, Argentina, 1996.Google Scholar
  12. [12]
    Zh. Liu. Detection of Transient Signal by Optimal Choice of a Wavelet, In Proc. IEEE Int. Conf. on ASSP, pp. 1553–1556, Dallas, Texas, 1994.Google Scholar
  13. [13]
    D. L. Jones and T. W. Parks. A High Resolution Data-Adaptive Time-Frequency Representation, IEEE trans. on ASSP, 38(12):2127–2135, 1990.CrossRefGoogle Scholar
  14. [14]
    J. P. Ovarlez, J. Bertrand, and P. Bertrand. Computations of Affine Time-Frequency Distributions using the Fast Mellin Transform, In Proc. IEEE Int. Conf. on ASSP, pp. V117–V120, San Francisco, California, 1992.Google Scholar
  15. [15]
    A. Papandreou and G. F. Boudreaux-Bartels. Generalization of the Choi-Williams Distribution and the Butterworth Distribution for Detection. IEEE Trans on ASSP, 41(l):463–472, 1993.CrossRefGoogle Scholar
  16. [16]
    O. Rioul and M. Vetterli, Wavelets and Signal Processing. IEEE Signal Processing Magazine, 8(4): 14–38, 1991.CrossRefGoogle Scholar
  17. [17]
    P. Saavedra and M. Iribarren. Machinery Dynamic Analysis using the Wigner-Ville Distribution (in Spanish). In Proc. V Argentinian Congress on Computational Mechanics, Tucuman, Argentina, 1996.Google Scholar
  18. [18]
    M. J. Shensa. The Discrete Wavelet Transform: Wedding the A-trous and Mallat Algorithms. IEEE Trans. on Signal Processing, 40(10):2464–2482, 1992.CrossRefMATHGoogle Scholar
  19. [19]
    R. G. Stockwell, L. Mansinha, and R. P. Lowe. Localization of the Complex Spectrum: The S transform. IEEE Trans. on Signal Processing, 44(4):998–1001, 1996.CrossRefGoogle Scholar
  20. [20]
    E. F. Velez. Spectral Estimation based on the Wigner-Ville Representation. Signal Processing, 20(4):325–347, 1990.CrossRefMATHGoogle Scholar
  21. [21]
    W. J. Williams. Reduced Interference Distributions: Biological Applications and Interpretations. In Proceedings of the IEEE, 84(9):1264–1280, 1996.CrossRefGoogle Scholar
  22. [22]
    Y. Zhao, L. E. Altes, and R. J. Marks. The Use of Cone-Shaped Kernels for Generalized Time-Frequency Representations of Nonstationary Signals. IEEE Trans. on ASSP, 38(7):1084–1091, 1990.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Marcelo Iribarren
    • 1
  • Cesar San Martin
    • 1
  • Pedro Saavedra
    • 1
  1. 1.Dept. of Electrical EngineeringUniversity of ConcepcióConcepcióChile

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