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Advances in Lee–Schetzen Method for Volterra Filter Identification

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Abstract

This paper concerns the identification of nonlinear discrete causal systems that can be approximated with the Wiener–Volterra series. Some advances in the efficient use of Lee–Schetzen (L–S) method are presented, which make practical the estimate of long memory and high order models. Major problems in L–S method occur in the identification of diagonal kernel elements. Two approaches have been considered: approximation of gridded data, with interpolation or smoothing, and improved techniques for diagonal elements estimation. A comparison of diagonal elements estimated, with different methods has been shown with extended tests on fifth order Volterra systems.

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References

  1. S. Boyd L. O. Chua (1998) ArticleTitle“Fading Memory and the Problem of Approximating Nonlinear Operators with Volterra Series” IEEE Transaction on Circuits Systems CAS-32 IssueID11 1150–1161

    Google Scholar 

  2. N. E. Cotter (1990) ArticleTitle“The Stone-Weierstrass Theorem and Its Application to Neural Networks” IEEE Transaction on Neural Networks 1 IssueID4 290–295

    Google Scholar 

  3. C. de Boor (1978) A Practical Guide to Splines Springer-Verlag New York

    Google Scholar 

  4. J. Dieudonné (1969) Foundations of Modern Analysis Academic Press New York

    Google Scholar 

  5. Y. Fang T.W.S. Chow (2000) ArticleTitle“Orthogonal Wavelet Neural Networks applying to Identification of Wiener Model” IEEE Transaction on Circuits Systems I 47 IssueID4 591–593

    Google Scholar 

  6. G.B. Giannakis E. Serpedin (2001) ArticleTitle“A Bibliography on Nonlinear System Identification” Signal Processing 81 533–580

    Google Scholar 

  7. G. O. A. Glentis P. Koukoulas N. Kalouptsidis (1999) ArticleTitle“Efficient Algorithms for Volterra System Identification” IEEE Transaction on Signal Processing 47 IssueID11 3042–3057

    Google Scholar 

  8. M.J. Korenberg (1991) ArticleTitle“Parallel Cascade Identification and Kernel Estimation for Nonlinear Systems” Annals of Biomedical Engineering 19 429–455 Occurrence Handle1:STN:280:By2D2svmtlA%3D Occurrence Handle1741525

    CAS  PubMed  Google Scholar 

  9. M.J. Korenberg S.B. Bruder P.J. McIlroy (1998) ArticleTitle“Exact Orthogonal Kernel Estimation from Finite Data Records: Extending Wiener’s Identification of Nonlinear Systems” Annals of Biomedical Engineering 16 201–214

    Google Scholar 

  10. M.J. Korenberg I.W. Hunter (1991) ArticleTitle“Identification of Nonlinear Biological Systems: LNL Cascade Models” Biological Cybernetics 55 125–134

    Google Scholar 

  11. Y.W. Lee (1960) Statistical Theory of Communication John Wiley and Sons New York and London

    Google Scholar 

  12. V.Z. Marmarelis (1978) ArticleTitle“Random versus Pseudorandom Test Signals in Nonlinear-System Identification” Proceeding of IEE 125 IssueID5 425–428

    Google Scholar 

  13. V.Z. Marmarelis (1997) ArticleTitle“Modeling Methodology for Nonlinear Physiological Systems” Annals of Biomedical Engineering 25 239–251 Occurrence Handle1:STN:280:ByiB3sbhsVU%3D Occurrence Handle9084829

    CAS  PubMed  Google Scholar 

  14. V.J. Mathews G.L. Sicuranza (2000) Polynomial Signal Processing John Wiley and Sons New York

    Google Scholar 

  15. R.D. Nowak R.G. Baraniuk (1999) ArticleTitle“Wavelet-Based Transformations for Nonlinear Signal Processing” IEEE Transaction on Signal Processing 47 IssueID7 1852–1865

    Google Scholar 

  16. R.D. Nowak B.D.V. Veen (1994) ArticleTitle“Random and Pseudorandom Inputs for Volterra Filter Identification” IEEE Transaction on Signal Processing 42 IssueID8 2124–2135

    Google Scholar 

  17. S. Orcioni, “Approximations and Analog Implementation of Nonlinear Systems Represented By Volterra Series,” In: Proceedings of 6th IEEE International Conference on Electronics, Circuits and Systems (ICECS99), vol. 2, Cyprus, 1999, pp. 1109–1113.

  18. S. Orcioni, M. Pirani, C. Turchetti, and M. Conti, “Practical notes on two Volterra filter identification direct methods,” In: Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS’02), vol. 3, Scottsdale, Arizona, 2002, pp. 587–590.

  19. G. Palm (1978) ArticleTitle“On Representation and Approximation of Nonlinear Systems” Biological Cybernetics 31 119–124

    Google Scholar 

  20. G. Palm (1979) ArticleTitle“On Representation and Approximation of Nonlinear Systems Part II: Discrete Time” Biological Cybernetics 34 49–52

    Google Scholar 

  21. G. Palm T. Poggio (1977) ArticleTitle“The Volterra Representation and the Wiener Expansion: Validity and Pitfalls” SIAM Journal of Applied Mathematics 33 IssueID2 195–216

    Google Scholar 

  22. G. Palm T. Poggio (1978) ArticleTitle“Stochastic Identification Methods for Nonlinear Systems: An Extension of the Wiener Theory” SIAM Journal of Applied Mathematics 34 IssueID3 524–534

    Google Scholar 

  23. T.M. Panicker J.V. Mathews (1998) ArticleTitle“Parallel-Cascade Realizations and Approximations of Truncated Volterra Systems” IEEE Transactions on Signal Processing 46 IssueID10 2829–2832

    Google Scholar 

  24. M. Pirani S. Orcioni C. Turchetti (2004) ArticleTitle“Diagonal Kernel Point Estimation of n-th Order Discrete Volterra-Wiener systems” EURASIP Journal on Applied Signal Processing 2004 IssueID12 1807–1816

    Google Scholar 

  25. I.W. Sandberg (1983a) ArticleTitle“The Mathematical Foundations of Associated Expansions for Mildly Nonlinear Systems” IEEE Transactions on Circuits System 30 IssueID7 441–455

    Google Scholar 

  26. I.W. Sandberg (1983b) ArticleTitle“On Volterra Expansions for Time-Varying Nonlinear Systems” IEEE Transactions on Circuits System 30 IssueID2 61–67

    Google Scholar 

  27. I.W. Sandberg, “Uniform Approximation with Doubly-Finite Volterra Series,” In: Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS91), 1991, pp. 754–757.

  28. I.W. Sandberg (1999) ArticleTitle“Separation Conditions and Approximation of Continuous-Time Approximately-Finite-Memory Systems” IEEE Transactions on Circuits System I 46 820–826

    Google Scholar 

  29. I.W. Sandberg L. Xu (1997) ArticleTitle“Uniform Approximation of Multidimensional Myopic Maps’ IEEE Transactions on Circuits System. I 44 IssueID6 477–485

    Google Scholar 

  30. I.W. Sandberg L. Xu (1998) ArticleTitle“Approximation of Myopic Systems Whose Inputs Need Not Be Continuous” Multidimensional Systems and Signal Processing 9 IssueID2 207–225

    Google Scholar 

  31. M. Schetzen (1974) ArticleTitle“A Theory of Non-Linear System Identification” International Journal of Control 20 IssueID4 577–592

    Google Scholar 

  32. M. Schetzen The Volterra and Wiener Theories of Nonlinear Systems. New York: John Wiley and Sons, 1980. R. Krieger 1989, Malabar, Florida edition.

  33. J.D. Victor (1987) ArticleTitle“The Fractal Dimension of a Test Signal: Implications for System Identification Procedures” Biological Cybernetics 57 421–426 Occurrence Handle1:STN:280:BieC3srgtFE%3D Occurrence Handle3435730

    CAS  PubMed  Google Scholar 

  34. V. Volterra (1959) Theory of Functionals and of Integrals and Integro-Differential Equations Dover Publications New York

    Google Scholar 

  35. D.T. Westwick B. Suki K.R Lutchen (1998) ArticleTitle“Sensitivity Analysis of Kernel Estimates: Implications in Nonlinear Physiological System Identification” Annals of Biomedical Engineering 26 488–501 Occurrence Handle1:STN:280:DyaK1c3jtVWmtA%3D%3D Occurrence Handle9570231

    CAS  PubMed  Google Scholar 

  36. N. Wiener (1958) Nonlinear Problems in Random Theory John Wiley New York

    Google Scholar 

  37. X. Zhao V.Z. Marmarelis (1998) ArticleTitle“Nonlinear Parametric Models from Volterra Kernels Measurements” Mathematical and Computer Modelling 27 37–43 Occurrence Handle1:CAS:528:DyaK1cXltlymsbo%3D Occurrence HandleMR1616792

    CAS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Elettronica, Intelligenza artificiale e Telecomunicazioni, Università Politecnica delle Marche, via Brecce Bianche 12, 60131, Ancona, Italy

    Simone Orcioni, Massimiliano Pirani & Claudio Turchetti

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  1. Simone Orcioni
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  2. Massimiliano Pirani
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  3. Claudio Turchetti
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Correspondence to Simone Orcioni.

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First Online Version Published in July, 2005

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Orcioni, S., Pirani, M. & Turchetti, C. Advances in Lee–Schetzen Method for Volterra Filter Identification. Multidim Syst Sign Process 16, 265–284 (2005). https://doi.org/10.1007/s11045-004-1677-7

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  • DOI: https://doi.org/10.1007/s11045-004-1677-7

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