Statistical analysis and spectral estimation techniques for one-dimensional chaotic signals

IEEE Transactions on Signal Processing

Volumn 45, Issue 6, 1997, Pages 1495-1506

  Isabelle, Steven H ^a   Wornell, Gregory W ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; CORRELATION THEORY; SPECTRUM ANALYSIS; STATISTICAL METHODS; WHITE NOISE;

MARKOV MAPS; ONE DIMENSIONAL CHAOTIC SIGNALS;

DIGITAL SIGNAL PROCESSING;

EID: 0031169888     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.599984     Document Type: Article

References (28)

1. A. V. Oppenheim, G. W. Wornell, S. H. Isabelle, and K. M. Cuomo, Signal processing in the context of chaotic signals, in Proc. Int. Conf. AcousL, Speech, Signal Processing, 1992.
2. A. Singer, G. Wornell, and A. Oppenheim, Nonlinear autoregressive modeling and estimation in the presence of noise, Digital Signal Processing, vol. 4, pp. 207-221, Oct. 1994.
3. H. C. Papadopoulos and G. W. Wornell, Maximum likelihood estimation of a class of chaotic signals, IEEE Trans. Inform. Theory, vol. 41, pp. 312-317, Jan. 1995.
4. M. D. Richard, Estimation and detection with chaotic systems, Ph.D. dissertation. Mass. Inst. Technol., Cambridge, Feb. 1994.
5. S. Haykin and X. B. Li, Detection of signals in chaos, Proc. IEEE, vol. 83, pp. 95-122, Jan. 1995.
6. S. H. Isabelle, A signal processing framework for the analysis and application of chaos, Ph.D. dissertation, Mass. Inst. Technol., Cambridge, Feb. 1995.
7. B. Chen and G. W. Wornell, Efficient channel coding for analog sources using chaotic systems, in Proc. IEEE GLOBECOM, Nov. 1996.
8. L. Risbo, On the design of tone-free sigma-delta modulators, IEEE Trans. Circuits Syst. II, vol. 42, pp. 52-55, Jan. 1995.
9. J. H. B. Deane and D. C. Hamill, Chaotic behavior in a current-mode controlled DC-DC converter, Electron. Lett., vol. 27, pp. 1172-1173, 1991.
10. C. Chase, J. Serrano, and P. J. Ramadge, Periodicity and chaos from switched flow systems: Contrasting examples of discretely controlled continuous systems, IEEE Trans. Automat. Contr., vol. 38, pp. 71-83, 1993.
11. L. O. Chua, Y. Yao, and Q. Yang, Generating randomness from chaos and constructing chaos with desired randomness, Int. J. Circuit Theory Applications, vol. 18, pp. 215-240, 1990.
12. K. Peterson, Ergodic Theory. Cambridge, U.K.: Cambridge Univ. Press, 1983.
13. I. P. Natanson, Theory of Functions of a Real Variable. New York: Frederick Ungar, 1961.
14. Y. S. Tang, A. I. Mees, and L. O. Chua, Synchronization and chaos, IEEE Trans. Circuits Syst., vol. CAS-30, pp. 620-626, Sept. 1983.
15. A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems. Cambridge, U.K.: Cambridge Univ. Press, 1985.
16. P. R. Halmos, Lectures on Ergodic Theory. Tokyo, Japan: Math. Soc. Japan, 1956.
17. A. Boyarsky and M. Scarowsky, On a class of transformations which have unique absolutely continuous invariant measures, Trans. Amer. Math. Soc., vol. 255, pp. 243-262, 1979.
18. R. Kaiman, Nonlinear aspects of sampled-data control systems, in Proc. Symp. Nonlinear Circuit Anal, Apr. 1956, pp. 273-313.
19. N. Friedman and A. Boyarsky, Matrices and eigenfunctions induced by Markov maps, Lin. Alg. App., vol. 39, pp. 141-147, 1981.
20. H. Mine, Nonnegative Matrices. New York: Wiley, 1988.
21. G. Strang, Linear Algebra and its Applications. New York: Academic, 1980, 2nd ed.
22. A. A. Kosyakin and E. A. Sandler, Ergodic properties of a class of piecewise-smooth transformations of a segment, Izv. VUZ Mat., vol. 118, pp. 32-40, 1972.
23. A. Boyarsky and G. Haddad, All invariant densities of piecewise linear raarkov maps are piecewise constant, Adv. Appl. Math., vol. 2, pp. 284-289, 1981.
24. H. Sakai and H. Tokumaru, Autocorrelations of a certain chaos, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-28, pp. 588-590, May 1980.
25. F. Hofbauer and G. Keller, Ergodic properties of invariant measures for piecewise monotonie transformations, Math, Z., vol. 180, pp. 119-140, 1982.
26. S. Wong, Some metric properties of mappings of the interval, Trans. Amer. Math. Soc., vol. 246, pp. 493-500, 1978.
27. P. Gora and A. Boyarsky, Compactness of invariant densities for families of expanding, piecewise monotonie transformations, Can. J. Math., vol. 41, no. 5, pp. 855-869, 1989.
28. A. Boyarsky, A matrix method for estimating the Lyapunov exponent of one dimensional systems, J. Stat. Phys., vol. 50, no. 1/2, pp. 213-229, 1988.