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.
Similar content being viewed by others
References
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)
Allen R.L., Mills D.W.: Signal Analysis—Time, Frequency, Scale and Structure. IEEE Press and Wiley, New York (2004)
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)
Choi J.H., Kim T.: Neural action potential detector using multi-resolution TEO. Electron. Lett. 38(12), 541–543 (2002)
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)
James W.: Principles of Psychology. Encyclopedia Britanica, Chicago (1990)
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)
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)
Picinbono, B.: Quadratic filters. In: Proceedings of IEEE International Confenrence on Acoustic Speech and Signal Processing, pp. 298–301 (1982)
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)
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)
Restrepo, A., Amarillo, C.: The root signals of Teager’s filter. Presented at Workshop on Nonlinear Signal and Image Processing, Baltimore, June (2001)
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)
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)
Sicuranza G.L.: Quadratic filters for signal processing. Procs. IEEE 80(8), 1263–1285 (1992)
Sandberg I.W.: Bounds for discrete-time Volterra series representations. IEEE trans. on CAS-1 46(1), 135–139 (1999)
Thurnhofer S., Mitra S.J., Sicuranza G.L.: Two-dimensional Teager filters, in Nonlinear Image Processing. Academic Press, San Diego (2001)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-010-0160-1