Skip to main content
SpringerLink
Log in

Root and pre-constant signals of the 1D Teager-Kaiser operator

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

We give an input/output characterization of the Teager-Kaiser operator, then we classify the root signals (those that remain invariant) and the pre-constant signals (those that produce a constant output) of the operator. With the gained knowledge, a simple detector of sinusoidal signals and of their corresponding frequencies is designed. The methods used allow for a certain amount of generalization providing a paradigm of sorts for the design of quadratic and other polynomial filters.

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. Atit, M., Hagan, J., Bansal, S., Ichord, R., Geocadin, R., Hansen, C., Sherman, D., Thakor, N.: EEG burst detection: performance evaluation. In: Proceedings of First Joint BMES/EMBS Conference vol. I, p. 441. Atlanta (1999)

  2. Allen R.L., Mills D.W.: Signal Analysis—Time, Frequency, Scale and Structure. IEEE Press and Wiley, New York (2004)

    Google Scholar 

  3. Cairns D.A., Hansen J.H.L., Riski J.E.: A non-invasice technique for detecting hypernasal speech using a nonlinear operator. IEEE Trans. Biomed. Eng. 43(1), 35–45 (1996)

    Article  Google Scholar 

  4. Choi J.H., Kim T.: Neural action potential detector using multi-resolution TEO. Electron. Lett. 38(12), 541–543 (2002)

    Article  MathSciNet  Google Scholar 

  5. Hamila R., Astola J., Alaya Cheikh F., Gabbouj M., Renfors M.: Teager energy and the ambiguity function. IEEE Trans. Signal Process. 47(1), 260–262 (1999)

    Article  Google Scholar 

  6. James W.: Principles of Psychology. Encyclopedia Britanica, Chicago (1990)

    Google Scholar 

  7. Kaiser, J.K.: On a simple algorithm to calculate the energy of a signal. In: Proceedings of IEEE International Confenrence on Acoustic Speech and Signal Processing, vol. I, pp. 381–384 (1990)

  8. Mitra, S., Li, H.: A new class of nonlinear filters for image enhancement. In: Proceedings of IEEE International Confenrence on Acoustic Speech and Signal Processing, pp. 2525–2527. Toronto, May (1991)

  9. Picinbono, B.: Quadratic filters. In: Proceedings of IEEE International Confenrence on Acoustic Speech and Signal Processing, pp. 298–301 (1982)

  10. Quiroga, J., Restrepo, A., Wedefort, L., Velasco, M.: On the 2D Teager-Kaiser operator. In: Proceedings of IEEE International Conference on Image Processing. vol. V, pp. 269–272. San Antonio, October (2007)

  11. Restrepo, A., Zuluaga, L., Ortiz, H., Ojeda, V.: Analytical properties of Teager’s filter. In: Proceedings of IEEE International Conference on Image Processing, vol. I, pp. 397–400. Santa Barbara (1997)

  12. Restrepo, A., Amarillo, C.: The root signals of Teager’s filter. Presented at Workshop on Nonlinear Signal and Image Processing, Baltimore, June (2001)

  13. Restrepo, A., Wedefort, L., Quiroga, J.: On the pre-constant of the Teager-Kaiser operator. In: Proceedings of IASTED International Conference on Circuit, Signal and Systems, pp. 15–19. Marina del Rey, CA, October (2005)

  14. Restrepo, A.: On conics, rational funtions and the Teager-Kaiser operator. Apuntes del XV Congreso de Matemáticas, Sociedad Colombiana de Matemáticas, Lect. Mat. Volumen Especial, pp. 105–114 (2006)

  15. Sicuranza G.L.: Quadratic filters for signal processing. Procs. IEEE 80(8), 1263–1285 (1992)

    Article  Google Scholar 

  16. Sandberg I.W.: Bounds for discrete-time Volterra series representations. IEEE trans. on CAS-1 46(1), 135–139 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  17. Thurnhofer S., Mitra S.J., Sicuranza G.L.: Two-dimensional Teager filters, in Nonlinear Image Processing. Academic Press, San Diego (2001)

    Google Scholar 

  18. Volterra, V.: Sopra le funzioni che dipendono da altre funzioni. Rend. Regia Accademia dei Lincei, 2O Sem., pp. 97–105, 141–146, 153–158 (1887)

  19. Zhou, G., Hansen, J.H.L., Kaiser, J.F.: Classification of speech under stress based on features derived from the nonlinear Teager energy operator. In: Proceedings of IEEE International Conference on Acoustic Speech and Signal Processing, pp. 549–552. Seattle, May (1998)

Download references

Author information

Authors and Affiliations

  1. Universidad de los Andes, Bogotá, Colombia

    Alfredo Restrepo

  2. Pontificia Universidad Javeriana, Bogotá, Colombia

    Julián Quiroga

Authors
  1. Alfredo Restrepo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julián Quiroga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alfredo Restrepo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Restrepo, A., Quiroga, J. Root and pre-constant signals of the 1D Teager-Kaiser operator. SIViP 5, 363–378 (2011). https://doi.org/10.1007/s11760-010-0160-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-010-0160-1

Keywords

Search

Navigation