Estimating the entropy of a signal with applications

IEEE Transactions on Signal Processing

Volumn 48, Issue 6, 2000, Pages 1687-1694

  Bercher, Jean François ^a  

^a Groupe ESIEE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ESTIMATION; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; RECURSIVE FUNCTIONS; REGRESSION ANALYSIS; SPECTRUM ANALYSIS;

BLIND DECONVOLUTION; SIGNAL ESTIMATION; SOURCE SEPARATION;

SIGNAL FILTERING AND PREDICTION;

EID: 0033738624     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.845926     Document Type: Article

References (26)

1. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. ]., vol. 27, pp. 379-23; 623-656, July/Oct. 1948 [Online] Available http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html.
2. P. Viola, N. N. Schraudolph, and T. J. Sejnowski, "Empirical entropy manipulation for real-world problems," in Advances in Neural Information Processing Systems 8. Cambridge, MA: MIT Press, 1996.
3. D. T. Pham, "Blind separation of instantaneous mixture of sources via an independent component analysis," IEEE Trans. Signal Processing, vol. 44, pp. 2768-2779, Nov. 1996.
4. R. Moddemeijer, "On estimation of entropy and mutual information of continuous distributions," Signal Process., vol. 16, no. 3, pp. 233-246, 1989.
5. I. Kontoyiannis et al., "Nonparametric entropy estimation for stationary processes and random fields, with application to english text," IEEE Trans. Inform. Theory, vol. 44, pp. 1319-1327, May 1998.
6. D. S. Ornstein and B. Weiss, "Entropy and data compression schemes," IEEE Trans. Inform. Theory, vol. 39, pp. 78-83, Jan. 1993.
7. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
8. P. Hall and S. Morton, "On the estimation of entropy," Ann. Inst. Stat. Math., vol. 45, pp. 69-88, 1993.
9. O. Vasicek, "A test of normality based on sample entropy," J. R. Stat. Soc. Ser. B, vol. 38, pp. 54-59, 1976.
10. J. C. Correa, "A new estimator of entropy," Commun. Stat.-Theory Methodol., vol. 24, pp. 2439-2449, 1995.
11. R. Wieczorkowski and P. Grzegorzewski, "Entropy estimators-Improvements and comparisons," Commun. Stat.-Simul. Comput., vol. 28, no. 2, pp. 541-567, 1999.
12. A. Pagès-Zamora and M. A. Eagunas, "New approaches in nonlinear signal processing: Estimation of the PDF function by spectral estimation methods," in Proc. IEEE-Athos Workshop Higher-Order Stat., June 1995, pp. 204-208.
13. S. Kay, "Model-based probability density function estimation," IEEE Signal Processing Lett., vol. 5, pp. 318-320, Dec. 1998.
14. J.-F. Bercher and C. Vignat, "Estimating the entropy of a signal with applications," in Proc. ICASSP, Phoenix, AZ, Mar. 1999.
15. A. Pagès-Zamora and M. A. Eagunas, "Fourier models for nonlinear signal processing," Signal Process., vol. 76, no. 1, pp. 1-16, 1999.
16. P. J. Brockwell and R. A. Davis, Times Series: Theory and Methods, 2nd ed. New York: Springer-Verlag, 1987.
17. J. Makhoul, "Einear prediction: A tutorial review," Proc. IEEE, vol. 63, pp. 561-580, Apr. 1975.
18. J. P. Burg, "Maximum entropy spectral analysis," presented at the Proc. 37th Meet. Soc. Explor. Geophys., 1967.
19. J. E. Shore, "Minimum cross-entropy spectral analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 230-237, Apr. 1981.
20. G. Kitagawa and W. Gersh, "A smoothness priors long AR model method for spectral estimation," IEEE Trans. Automat. Contr., vol. AC-30, pp. 57-65, 1985.
21. J.-F. Giovannelli, G. Demoment, and A. Herment, "A bayesian method for long AR spectral estimation: A comparative study," IEEE Trans. Ultrason. Freq. Ferroelect., vol. 43, pp. 220-233, Mar. 1996.
22. A. V Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
23. O. Hössjer and U. Host, "On-line density estimators with high efficiency," IEEE Trans. Inform. Theory, vol. 41, pp. 829-835, May 1995.
24. S. Haykin, Adptive Filter Theory, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.
25. D. Donoho, "On minimum entropy deconvolution," in Applied Time Series Analysis II. New York: Academic, 1981, pp. 565-609.
26. A. Dembo and T. M. Cover, "Information theoretic inequalities," IEEE Trans. Inform. Theory, vol. 37, pp. 1501-1518, Nov. 1991.