Time-Frequency and Time-Scale Signal Analysis by Harmonic Wavelets

  • David E. Newland
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

New details of the theory of harmonic wavelets are described and provide the basis for computational algorithms designed to compute high-definition time-frequency maps. Examples of the computation of phase using the complex harmonic wavelet and methods of signal segmentation based on amplitude and phase are described.

Keywords

Wavelet Analysis Wavelet Coefficient Vibration Analysis Differential Phase Frequency Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L. Cohen. Time-Frequency Analysis. Prentice Hall, New Jersey, 1995.Google Scholar
  2. [2]
    C. H. Hodges, J. Power, and J. Woodhouse. The Use of the Sonogram in Structural Acoustics and an Application to the Vibrations of Cylindrical Shells. J. Sound Vib., 101:203–218, 1985.CrossRefGoogle Scholar
  3. [3]
    P. J. Loughlin and G. D. Bernard. Cohen-Posch (positive) time-frequency distributions and their application to machine vibration analysis. Mech. Systems & Signal Processing, 11:561–576, 1997.CrossRefGoogle Scholar
  4. [4]
    W. D. Mark. Spectral analysis of the convolution and filtering of non-stationary stochastic processes. J. Sound Vib., 11:19–63, 1970.CrossRefMATHGoogle Scholar
  5. [5]
    D. E. Newland. Mechanical Vibration Analysis and Computation. Addison Wesley Longman, 1989.Google Scholar
  6. [6]
    D. E. Newland. Harmonic Wavelet Analysis. Proc. R. Soc. Lond. A, 443:203–225, 1993.CrossRefMATHGoogle Scholar
  7. [7]
    D. E. Newland. Random Vibrations, Spectral and Wavelet Analysis, 3rd edition. Addison Wesley Longman, 1993.Google Scholar
  8. [8]
    D. E. Newland. Harmonic and Musical Wavelets. Proc. R. Soc. Lond. A, 444:605–620, 1994.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    D. E. Newland. Wavelet Analysis of Vibration, Part 1: Theory. J. Vibration & Acoustics, Trans. ASME, 116:409–416, 1994.CrossRefGoogle Scholar
  10. [10]
    D. E. Newland. Wavelet Analysis of Vibration, Part 2: Wavelet Maps. J. Vibration & Acoustics, Trans. ASME, 116:417–425, 1994.CrossRefGoogle Scholar
  11. [11]
    D. E. Newland. Wavelet Theory and Applications. In Proc. 3rd Int. Congress on Sound and Vibration, Montreal, Canada (published by Int. Science Publications, AL, USA), pp. 695-713, 1994. Reprinted as Wavelet Analysis of Vibration Signals, Part 1. Int. J. Acoustics and Vib., 1(1): 11–16, 1997.Google Scholar
  12. [12]
    D. E. Newland. Time-Frequency Analysis by Harmonic Wavelets and by the Short-Time Fourier Transform. In Proc. 4th Int. Congress on Sound and Vibration, St. Petersburg, Russia (published by Int. Science Publications, AL, USA), 3, pp. 1975–1982, 1996. Reprinted as Wavelet Analysis of Vibration Signals, Part 2. Int. J. Acoustics and Vib., 2(1):21-27, 1997.Google Scholar
  13. [13]
    D. E. Newland. Practical signal analysis: Do wavelets make any difference? In Proc. 1997 ASME Design Engineering Technical Conferences, 16th Biennial Conf. on Vibration and Noise, Paper DETC97/VIB-4135 (CD ROM ISBN 0 7918 1243 X), Sacramento, California, 1997.Google Scholar
  14. [14]
    D. E. Newland. Application of Harmonic Wavelets to Time-Frequency Mapping. In Proc. 5th Int. Congress on Vibration and Acoustics, 4, pp. 2043–2054 (Paper No. 260, CD ROM ISBN 1 876346 06 X), University of Adelaide, Australia, 1997.Google Scholar
  15. [15]
    C. Tait and W. Findlay. Wavelet Analysis for Onset Detection. In Proc. Int. Computer Music Conf, ICMA, Hong Kong, pp. 500–503, 1996.Google Scholar
  16. [16]
    J. Ville. Théorie et Applications de la Notion de Signal Analytique. Câbles et Transmission, 2:61–74, 1948.Google Scholar
  17. [17]
    E. P. Wigner. On the Quantum Correction for Thermodynamic Equilibrium. Physical Review Letters, 40:749–759, 1932.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • David E. Newland
    • 1
  1. 1.Department of EngineeringUniversity of CambridgeCambridgeUK

Personalised recommendations