Skip to main content
SpringerLink
Log in

New Methods of Time-Frequency Analysis

  • Chapter
Transforms and Fast Algorithms for Signal Analysis and Representations

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

  • 660 Accesses

Abstract

This chapter presents two new transforms that are useful for the analysis of time-varying signals.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. B. Almeida, The fractional Fourier transform and time-frequency representations, IEEE Trans. Signal Process., vol. 42, no. 11, 3084–3091, 1994.

    Article  Google Scholar 

  2. L. Auslander and R. Tolimieri, Radar ambiguity function and group theory, SIAM J. Math. Anal, vol. 165, no. 3, 577–601, 1985.

    Article  MathSciNet  Google Scholar 

  3. J. Bertrand and P. Bertrand, Affine time-frequency distributions, in Time-Frequency Signal Analysis - Methods and Applications, ed. B. Boashash, Longman-Chesire, Mel-bourne, Australia, 1991.

    Google Scholar 

  4. F. Blawatsch, Duality and classification of bilinear time-frequency signal representations, IEEE Trans. Signal Process., vol. 39, no. 7, 1564–1574, 1991.

    Article  Google Scholar 

  5. T. A. C. M. Claasen and W. F. G. Mecklenbrauker, The Wigner distribution - a tool for time-frequency signal analysis - Part I: Continuous-time signals, Philips J. Res., vol. 35, 217–250, 1980.

    MathSciNet  MATH  Google Scholar 

  6. T. A. C. M. Claasen and W. F. G. Mecklenbrauker, The Wigner distribution - a tool for time-frequency signal analysis - Part III: Relations with other time-frequency signal transformations, Philips J. Res., vol. 35, no. 6, 372–389, 1980.

    MathSciNet  MATH  Google Scholar 

  7. L. Cohen, Time-frequency distributions - a review, Proc. IEEE, vol. 77, no. 7, 941–981, 1989.

    Article  Google Scholar 

  8. M. F. Erden, M. A. Kutay and H. M. Ozaktas, Repeated filtering in consecutive frac-tional Fourier domains and its application to signal restoration, IEEE Trans. Signal Process., vol. 47, no. 5, 1458–1462, 1999.

    Article  Google Scholar 

  9. P. Flandrin, Time-frequency processing of bat sonar signals, animal sonar systems sym-posium, Helsinger (DK), Sept. 10–19. 1986, also in Animal Sonar - Processes and Performance, P. E. Nachtigall and P.W.B. Moore eds., 797–802, Plenum Press, New York, 1988.

    Google Scholar 

  10. O. D. Grace, Instantaneous power spectra, J. Acoust Soc. Ant., vol. 69, 191–198, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  11. F. Hlawatsch and P. Flandrin, The interference structure of the Wigner distribution and related time-frequency signal representatins, in The Wigner Distribution - Theory and Applications in Signal Processing, W. Mecklenbrauker, ed., Elsevier Science Publishers, North Holland, 1992.

    Google Scholar 

  12. H. Inuzuka, T. Ishiguroand and S. Mizuno, Elimination of cross-components in the Wigner distribution of the exponentially swept data by varying the sampling rate, Con- ference Record - IEEE Instrumentation & Measurement Technology, 2, 717–720, 1994.

    Google Scholar 

  13. D. L. Jones and T. W. Parks, A high resolution data-adaptive time-frequency repre-sentation, IEEE Trans. Acoust, Speech. Signal. Process., vol. 38, no. 12, 2127–2135, 1990.

    Article  Google Scholar 

  14. D. L. Jones and T. W. Parks, A resolution comparison of several time-frequency repre-sentations, IEEE Trans. Signal Process., vol. 40, no. 2, 413–420, 1992.

    Article  Google Scholar 

  15. S. Kadamte and G. F. Boudreaux-Bartels, A comparison of the existence of ‘cross terms’ in the Wigner distribution and the squared magnitude of the wavelet transform and the short-time Fourier transform, IEEE Trans. Signal Process., vol. 40, no. 10, 2498–2517, 1992.

    Article  Google Scholar 

  16. A. S. Kayhan, A. El-Jaroudi and L. F. Chaparro, Data-adaptive evolutionary spectral estimation, IEEE Trans. Signal Process., vol. 43, no. 1, 204–213, 1995.

    Article  Google Scholar 

  17. J. R. Kiauder, A. C. Price, S. Darlinglon and W. J. Albersheim, The theory and design of chirp radars, Bell System Tech. J., vol. 39, 745–808, 1960.

    Google Scholar 

  18. A. W. Lohmann and B. H. Soffer, Relationships between the Radon-Wigner and frac-tional Fourier transforms, J. Opt. Soc. Amer. A., vol. 11 no. 6, 1798–1801, 1994.

    Article  MathSciNet  Google Scholar 

  19. S. V. Marid and E. L. Titlebaum, Frequency hop multiple access codes based upon the theory of cubic congruences, IEEE Trans. Aerospace, Elect. Syst, vol. 26, no. 6, 1035–1039, 1990.

    Article  Google Scholar 

  20. W. F. G. Mecklenbráuker, A tutorial on non-parametric bilinear time-frequency signal representations, Les Houches, Session XLV, 1985, Signal Processing, eds, J. L. Lacoume, T. S. Durrani and R. Stora, 277–336, 1987.

    Google Scholar 

  21. G. Mourgues, M. R. Feix, J. C. Andrieux and P. Bertrand, Not necessary but sufficient conditions for the positivity of generalized Wigner functions, J. Math. Phys., vol. 26, 2554–2555, 1985.

    Article  MathSciNet  Google Scholar 

  22. S. N. Nawab and T. F. Quatieri, Advanced Topics in Signal Processing, J. S. Lim and A. N. Oppenheim. eds., Prentice-Hall, Englewood Cliffs, NJ, 1988.

    Google Scholar 

  23. H. M. Ozaktas and D. Mendlovic, The fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators, Opt. Lett, vol. 19, 1678–1680, 1994.

    Article  Google Scholar 

  24. A. Papoulis, Signal Analysis, McGraw-Hill Book Co., New York. 1977.

    MATH  Google Scholar 

  25. P. Pellat-Finet and G. Bonnet, Fractional-order Fourier transform and Fourier optics, Opt Commun., vol. 111, 141–154, 1994.

    Article  Google Scholar 

  26. S. Qian and D. Chen, Joint time-frequency analysis: methods and applications, Prentice Hall PTR, Upper Saddle River, NJ, 1996.

    Google Scholar 

  27. S. Qian and J. M. Morris, Wigner distribution decomposition and cross-terms deleted representation, Signal Processing, vol. 27, no. 2, 125–144, 1992.

    Article  MATH  Google Scholar 

  28. L. Qiu, Elimination of the cross-term for two-component signals in the Wigner distribu-tion, International J. of Electronics, vol. 78. 1091–1099, 1995.

    Article  Google Scholar 

  29. L. R. Rabiner and R. W. Schafer, Digital Processing of Speech Signals, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1978.

    Google Scholar 

  30. G. N. Ramachandran and A. V. Lakshminarayanan, Three dimensional reconstruc-tions from radiographs and electron micrographs: Application of convolution instead of Fourier transforms, Proc. Nat. Acad. Sci., vol. 68, 2236–2240, 1971.

    Article  MathSciNet  Google Scholar 

  31. I. Raveh and D. Mendlovic, New properties of the Radon transform of the cross Wigner ambiguity distribution function, IEEE Trans. Signal Process., vol. 47, no. 7, 2077–2080, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  32. M. G. Raymer, M. Bech and D. F. Mcalister, Complex wave-field reconstruction using phase-space tomography, Phys. Rev. Lett, vol. 72, 1137–1140, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  33. A. W. Rihaczek, Design of zigzag FM zignals, IEEE Trans. AER EL, vol. AES-4, 1968.

    Google Scholar 

  34. O. Rioul and P. Flandrin, Time-scale energy distributions: a general class extending wavelet transforms, IEEE Trans. Signal Process., vol. 40, no. 7, 1746–1757, 1992.

    Article  MATH  Google Scholar 

  35. B. Ristic and B. Boashash, Kernel design for time-frequency signal analysis using the Radon transform, IEEE Trans. Signal Process., vol.41, no. 5, 1996–2008, 1993.

    Article  MATH  Google Scholar 

  36. L. A. Shepp and B. F. Logan, The Fourier reconstruction of a head section, IEEE Trans. Nucl. Sci., vol. NS-21, 21–43, 1974.

    Google Scholar 

  37. D. T. Smithey, M. Beck and M. G. Raymer, Measurement of the Wiger distribution and the density matrix of a light mode using optical homodyne tomography application to squeezed states and the vacuum, Phys. Rev. Lett, vol. 70, 1244–1247, 1993.

    Article  Google Scholar 

  38. L. Stankovic, Method for improved distribution concentration in the time-frequency analysis of multicomponent signals using the L-Wigner distribution, IEEE Trans. Signal Process, vol. 43, no. 5, 1262–1268, 1995.

    Article  Google Scholar 

  39. H. H. Szu and J. A. Blodgett, Wigner distribution and ambiguity function, in Optics in Four Dimensions, ed. L. M. Narducci, American Institute of Physics, New York, pp. 355–81, 1981.

    Google Scholar 

  40. H. L. VanTrees, Detection, Estimation and Modulation Theory, Part III, J. Wiley & Sons Publ., New York, 1971.

    Google Scholar 

  41. X. G. Xia, Y. Owechko, B. H. Soffer and R. M. Matic, On generalized-marginal time-frequency distributions, IEEE Trans. Signal Process., vol.44, no. 11, 2882–2886, 1996.

    Article  Google Scholar 

  42. A. L. Warrick and P. A. Delaney, Detection of linear features using a localized Radon transform with a wavelet filter, ICASSP-97, vol. 4, 2769–2772, 1997.

    Article  Google Scholar 

  43. J. C. Wood and 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., vol. 42, no. 8, 2094–2104, 1994.

    Article  Google Scholar 

  44. J. C. Wood and D. T. Barry, Linear signal synthesis using the Radon-Wigner transform, IEEE Trans. Signal Process., vol. 42, no. 8, 2105–2111, 1994.

    Article  Google Scholar 

  45. J. C. Wood and D. T. Barry, Radon transformation of time-frequency distributions for analysis of multicomponent signals, IEEE Trans. Signal Process., vol. 42, no. 11, 3166–3177, 1994.

    Article  Google Scholar 

  46. J. C. Wood and D. T. Barry, Time-frequency analysis of skeletal muscle and cardiac vibrations, Proceedings of the IEEE, vol. 84, no. 9, 1281–1294, 1996.

    Article  Google Scholar 

  47. F. Zhang, G. Bi and Y. Chen, Tomography time-frequency transform, IEEE Trans. Signal Process, vol. 50, no. 6, 1289–1297, 2002.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technical University, Singapore, 63798, Singapore

    Guoan Bi

  2. Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong

    Yonghong Zeng

Authors
  1. Guoan Bi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yonghong Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bi, G., Zeng, Y. (2004). New Methods of Time-Frequency Analysis. In: Transforms and Fast Algorithms for Signal Analysis and Representations. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8220-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-0-8176-8220-0_9

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6499-6

  • Online ISBN: 978-0-8176-8220-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation