Measuring Volterra Kernels

IEEE Transactions on Circuits and Systems

Volumn 30, Issue 8, 1983, Pages 571-577

  Boyd, Stephen ^a   Tang, Y S ^a   Chua, Leon O ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SYSTEMS ANALYSIS;

NONLINEAR SYSTEMS; VOLTERRA KERNELS;

MATHEMATICAL TECHNIQUES;

EID: 0020806844     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCS.1983.1085391     Document Type: Article

References (33)

1. I. W. Sandberg, “Expansions for nonlinear systems,” Bell Syst. Tech. J., vol. 61, pp. 159-200, Feb. 1982.
2. C. Lesiak and A. J. Krener, “Existence and uniqueness of Volterra series,” IEEE Trans. Automat. Contr., vol. AC-23, pp. 1090-1095, Dec. 1978.
3. B. J. Leon and D. J. Schaefer, “Volterra series and Picard iteration for nonlinear circuits and systems,” IEEE Trans. Circuits Syst., vol. CAS-25, pp. 789-793, Sept. 1978.
4. R. DeFigueiredo and T. Dwyer, “A best approximation framework and implementation for simulation of large scale nonlinear systems,” IEEE Trans. Circuits Syst., vol. CAS-27, pp. 1005-1014, Nov. 1980.
5. M. Fliess, “A note on Volterra series for nonlinear differential systems,” IEEE Trans. Automat. Contr., vol. AC-25, pp. 116-117, Feb. 1980.
6. A. Halme, J. Orava, and H. Blomberg, “Polynomial operators in nonlinear systems theory,” Int. J. Syst. Sci., vol. 2, no. 1, pp. 25-47, 1971.
7. N. Wiener, Nonlinear Problems in Random Theory. Cambridge, MA: MIT Press, 1958.
8. M. B. Brilliant, “Theory of the analysis of nonlinear systems,” MIT RLE Rep. 345, Mar. 1958.
9. R. H. Flake, “Volterra series representation of nonlinear systems,” IEEE Trans. Appl. Ind., vol. 81, pp. 330-335, Jan. 1963.
10. J. F. Barrett, “The use of functionals in the analysis of nonlinear physical systems,” J. Electronic Control, vol. 15, pp. 567-615, 1963.
11. J. K. Lubbock and V. S. Bansal, “Multidimensional Laplace transform for synthesis of nonlinear systems,” Proc. Inst. Elect. Eng., vol. 116, pp. 2075-2082, Dec. 1969.
12. L. O. Chua and C. Y. Ng, “Frequency domain analysis of nonlinear systems: general theory,” IEE Journal Electron. Circuits Systems, vol. 3, no. 4, pp. 165-185, July 1979.
13. L. O. Chua and C. Y. Ng, “Frequency domain analysis of nonlinear systems: Formulation of transfer functions,” IEE Journal Electron. Circuits Syst., vol. 3, no. 6, pp. 257-267, Nov. 1979.
14. E. Bedrosian and S. O. Rice, “Output properties of Volterra systems driven by harmonic and Gaussian inputs,” Proc. IEEE, vol. 59, pp. 1688-1707, Dec. 1971.
15. G. Palm and T. Poggio, “The Volterra expansion and the Wiener expansion: Validity and pitfalls,” SIAM J. Appl. Math., vol. 33, pp. 195-216, 1977.
16. R. J. Roy and J. Sherman, “A learning technique for Volterra series representation,” IEEE Trans. Automat. Contr., vol. AC-12, pp. 761-764, Dec. 1967.
17. E. J. Ewen and D. D. Weiner, “Identification of weakly nonlinear systems using input and output measurements,” IEEE Trans. Circuits Syst., vol. CAS-27, pp. 1255-1261, Dec. 1980.
18. Y. W. Lee and M. Schetzen, “Measurement of Wiener kernels of a nonlinear system by crosscorrelation,” Int. J. Contr., vol. 2, no. 3, pp. 237-254, 1965.
19. J. Aracil, “Measurement of Wiener kernels with binary random signals,” IEEE Trans. Automat. Contr., vol. AC-15, pp. 123-125, Feb. 1970.
20. R. J. Simpson and H. M. Power, “Correlation techniques for the identification of nonlinear systems,” Measurement and Control, vol. 5, pp. 316-321, Aug. 1972.
21. H. A. Barker, S. N. Obidegwu, and T. Pradisthayou, “Performance of antisymmetric pseudorandom signals in the measurement of second order Volterra kernels,” Proc. Inst. Elect. Eng., vol. 119, pp. 353-362, Mar. 1972.
22. S. Narayanan, “Application of Volterra series to intermodulation distortion of transistor feedback amplifiers,” IEEE Trans. Circuit Theory, vol. CT-17, pp. 518-527, Nov. 1970.
23. S. Narayanan, “Transistor distortion using Volterra series representation,” Bell Syst. Tech. J., vol. 46, pp. 991-1023, May-June 1967.
24. S. Narayanan, “Intermodulation distortion of cascaded transistors,” IEEE Trans. Solid-State Circuits, vol. SC-4, pp. 97-106, June 1969.
25. R. G. Meyer, M. J. Hensa, and R. Eschenbach, “Crossmodulation and intermodulation in amplifiers at high frequencies,” IEEE Trans. Solid-State Circuits, vol. SC-7, pp. 16-23, Feb. 1972.
26. D. D. Weiner and J. Spina, Sinusoidal Analysis and Modelling of Weakly Nonlinear Circuits. New York: Van Nostrand, 1980.
27. G. Heng, L. Stark, and P. Eykhoff, “On the interpretation of kernels,” Ann. Biomed. Eng., vol. 5, pp. 130-143, 1977.
28. J. Victor and R. Shapley, “A method of nonlinear analysis in the frequency domain,” Biophysical J., vol. 29, pp. 459-484, Mar. 1980.
29. H. J. Wertz, “On the numerical inversion of a recurrent problem: The Vandermonde matrix,” IEEE Trans. Automat. Contr., vol. AC-10, p. 492, Oct. 1965.
30. W. T. Nye, E. Polak, A. L. Sangiovanni-Vincentelli, and A. L. Tits, “DELIGHT: An optimization-based computer-aided design system,” presented at 1981 IEEE Int. Symp. Circuits and Systems, Apr. 1981.
31. D. M. Leskiw and K. S. Miller, “Convergence of polynomial least-squares estimators,” Proc. IEEE, vol. 70, pp. 520-522, May 1982.
32. F. Proshan, “Precision of least-squares polynomial estimates,” SIAM Rev., vol. 3, no. 3, July 1961.
33. P. Z. Peebles, Jr., “An alternate approach to the prediction of polynomial signals in noise from discrete data,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-6, no. 4, pp. 534-543, July 1970.