Skip to main content
SpringerLink
Log in

The running time-frequency distributions

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

This paper introduces the running kernels that yield recursive structures for time-frequency distributions (TFDs). The running kernels offer important properties not possessed by the commonly used block distribution kernels. The introduced kernels allow an invariance in computations with respect to the extent of the kernel in the time or the lag variable. However, contrary to the wide class of block kernels that satisfy the desired timefrequency (t-f) properties, most recursive (running) time-frequency distributions (RTFDs) violate the marginal and the support properties. This paper considers both the direct and the indirect types of recursion and presents examples for illustration.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Ahmed and S. Vijayendra, An adaptive short term correlation algorithm,Proceedings of the International Conference on Acoustics, Speech and Signal Processing, Boston, MA, 1983.

  2. J. B. Allen and L. R. Rabiner, A unified approach to short-time Fourier analysis and synthesis,Proceedings of the IEEE, vol. 65, November 1977.

  3. M. Amin, Time-frequency spectral analysis and estimation for nonstationary random processes, inTime-Frequency Signal Analysis: Methods and Applications, B. Boashash, ed., Longman Cheshire, Australia, 1992.

    Google Scholar 

  4. M. Amin, Spectral smoothing and recursion based on the nonstationarity of the autocorrelation function,IEEE Transactions in Signal Processing, vol. 39, no. 1, January 1991.

  5. M. Amin, Mixed time-based power spectrum estimation,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 36, no. 5, pp. 739–750, May 1988.

    Google Scholar 

  6. M. Amin, Computationally lag-invariant recursive power spectrumestimation,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 35, no. 12, pp. 1713–1724, December 1987.

    Google Scholar 

  7. M. Amin, Time-varying spectrum estimation for a general class of nonstationary processes,Proceedings of IEEE, vol. 74, no. 12, pp. 1800–1802, December 1986.

    Google Scholar 

  8. J. C. Andrieux, M. R. Feix, G. Mourgues, P. Betrand, B. Izrar, and V. Nguyen, Optimum smoothing of the Wigner-Ville distribution,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 24, pp. 764–769, June 1987.

    Google Scholar 

  9. T. Barnwell, Recursive windowing for generating autocorrelation coefficients for LPC analysis,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 29, no. 5, pp. 1062–1066, October 1981.

    Google Scholar 

  10. B. Boashash and P. Black, An efficient real-time implementation in Wigner distribution,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 35, no. 11, pp. 1611–1618, November 1987.

    Google Scholar 

  11. I. Choi and W. Williams, Improved time-frequency representation of multicomponent signals using exponential kernels,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 37, no. 6, pp. 862–971, April 1989.

    Google Scholar 

  12. T. A. C. M. Claasen and W. F. G. Mecklenbrauker, The Wigner distribution—A tool for time frequency signal analysis-Part II: Discrete-time signals,Philips Journal of Research, vol. 35, no. 4–5, October 1980, pp. 276–300.

    Google Scholar 

  13. P. Flandrin, Some features of time-frequency representations of multicomponent signals,Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, San Diego, CA, March 1984.

  14. P. Flandrin and B. Escudie, An interpretation of the pseudo-Wigner-Ville distribution,Signal Processing, vol. 6, no. 1, pp. 27–36, January 1984.

    Google Scholar 

  15. H. Garudadri, M. Beddoes, A. Benguerel, and J. Gilbert, On computing the smoothed Wigner distribution,Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Dallas, TX, 1987.

  16. J. Makhoul and L. Cosell, Adaptive lattice analysis of speech,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 29, no. 3, pp. 654–659, June 1981.

    Google Scholar 

  17. W. Martin and P. Flandrin, Detection of changes of signal structures by using the Wigner-Ville spectrum,Signal Processing, vol. 8, no. 2, pp. 215–233, 1985.

    Google Scholar 

  18. V. Mathews, D. Youn, and N. Ahmed, A unified approach to nonparametric spectrum estimation algorithms,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 35, no. 3, pp. 338–350, March 1987.

    Google Scholar 

  19. A. H. Nuttal and G. C. Carter, Spectral estimation using combined time and lag weighting,Proceedings of IEEE, September 1982.

  20. W. Porter, Computational aspects of quadratic signal processing,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 38, no. 1, pp. 137–144, January 1990.

    Google Scholar 

  21. M. Portnoff, Time-frequency representation of digital signals and systems based on short-time Fourier analysis,IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 1, no. 28, pp. 55–69, February 1980.

    Google Scholar 

  22. M. Sun, C. Li, L. Sekhar, and R. Sclabassi, Efficient computation of the discrete pseudo-Wigner distribution,IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 11, pp. 1735–1742, November 1989.

    Google Scholar 

  23. M. Unser, Recursion in short-time signal analysis,Signal Processing, vol. 5, pp. 229–240, 1983.

    Google Scholar 

  24. Y. Zhao, L. Atlas, and R. Marks, II, The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals,IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, no. 7, pp. 1084–1091, July 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Villanova University, 19085, Villanova, PA

    Moeness G. Amin

Authors
  1. Moeness G. Amin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by the US Air Force, grant no. AFOSR F49620-93-C0063 and a grant from the Office of Research and Sponsored Projects at Villanova University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Amin, M.G. The running time-frequency distributions. Circuits Systems and Signal Process 14, 401–414 (1995). https://doi.org/10.1007/BF01189018

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01189018

Keywords

Search

Navigation