Nonlinear System Modeling Based on the Wiener Theory

Proceedings of the IEEE

Volumn 69, Issue 12, 1981, Pages 1557-1573

  Schetzen, Martin ^a  

^a NORTHEASTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NONLINEAR SYSTEM MODELING;

SYSTEMS SCIENCE AND CYBERNETICS;

MATHEMATICAL MODEL; NONBIOLOGICAL MODEL; NONLINEAR SYSTEM; PSYCHOLOGICAL ASPECT;

EID: 0019806963     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1981.12201     Document Type: Article

References (21)

1. N. Wiener, Nonlinear Problems in Random Theory. New York: Technology Press, M.I.T. and Wiley, 1958.
2. Y. W. Lee and M. Schetzen, “Measurement of the Wiener kernels of a nonlinear system by cross-correlation,” Int. J. Contr., vol. 2, no. 3, pp. 237-254, Sept. 1965.
3. M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems. New York: Wiley, 1980.
4. V. Volterra, “Sopra le funzioni che dipendone de altre funzioni,” Rend. R. Academia dei Lincei 2° Sem, pp. 97-105, 141-146, and 153-158, 1887.
5. —, Lecons sur les Fonctions De Lignes. Paris, France: Gaunthier-Villars, 1913.
6. –, Theory of Functionals and of Integral and Integro-Differential Equations. New York: Dover, 1959.
7. M. Schetzen, “Measurement of the kernels of a nonlinear system of finite order,” Int. J. Contr., vol. 1, no. 3, pp. 251-263, Mar. 1965; Corrigendum, vol. 2, no. 4, p. 408, Oct. 1965.
8. M. Frechet, “Sur lea foncionelles continues,” Annales Scientifiques de L'Ecole Normale Superieure, 3rd ser., vol. 27, pp. 193-216, 216, May 1910.
9. Y. W. Lee, “Contributions of Norbert Wiener to linear theory and nonlinear theory in engineering,” in Selected Papers of Norbert Wiener. Cambridge, MA: Soc. for Indust. and Appl. Mathemat. and M.I.T. Press, 1964, p. 24.
10. A. G. Bose, “A theory of nonlinear systems,” Tech. Rep. 309, Research Lab. of Electron., M.I.T., 1956.
11. M. Schetzen, “A theory of nonlinear system identification,” Int. J. Contr., vo l. 20, no. 4, pp. 577-592, Oct., 1974.
12. G. Hung and L. Stark, “The kernel identification method—review of theory, calculation, application, and interpretation,” Math. Biosci., vol. 37, pp. 135-170, 1977.
13. P. Z. Marmarelis and V. Z. Marmarelis, Analysis of Physiological Systems—The White Noise Approach. New York: Plenum, 1978.
14. A. S. French and E. G. Butz, “Measuring the Wiener kernels of a nonlinear system using the fast Fourier transform algorithm,” Int. J. Contr., vol. 17, no. 3, pp. 529-539, Mar. 1973.
15. M. Schetzen, “Determination of optimum nonlinear systems for generalized error criteria based on the use of gate functions,” IEEE Trans. Inform. Theory, vol. 11, no. 1, pp. 117-125, Jan. 1965
16. S. A. Billings, “Identification of nonlinear systems—A survey,” Proc. Inst. Elec. Eng., vol. 127, part D, no. 6, pp. 272-285, Nov. 1980.
17. J. F. Barrett, “A bibliography on Volterra series, Hermite functional expansions, and related subjects,” T. H. Rep. 77-E-71, Eindhoven University of Technology, second revised version, Mar. 1980.
18. H. Ogura, “Orthogonal functionals of the Poisson process,” IEEE Trans. Inform. Theory, vol. 18, pp. 473-481, July 1972.
19. A. Segall and T. Kailath, “Orthogonal functionals of independent-increment increment processes,” IEEE Trans. Inform. Theory, vol. 22, pp. 287-298, May, 1976.
20. H. I. Krausz, “Identification of nonlinear systems using random impulse train inputs,” Biolog. Cybern., vol. 19, pp. 217-230, 1975.
21. K. L. Jordan, “Discrete representation of random signals,” Tech. Rep. 378, Research Lab. Electron., M.I.T., 1961.