- BENDAT , J. S. 1990 . Nonlinear System Analysis and Identification , Wiley : New York .
- BIGLIERI , E. , BARBERIS , S. and CATENA , M. 1988 . Analysis and compensation of non-linearities in digital transmission systems . IEEE Journal on Selected Areas Communication , 6 : 42 – 51 .
- BILLINGS , S. A. 1980 . Identification of non-linear systems-a survey . Proceedings of the IEE. , 127 : 272 – 285 .
- BILLINGS , S. A. and FAKHOURI , S. Y. 1982 . Identification of systems containing linear dynamic and static non-linear elements . Automatica , 18 : 15 – 26 .
- CAI , T. T. 1999 . Adaptive wavelet estimation: a block thresholding and oracle inequality approach . Annals of Statistics. , 27 : 898 – 924 .
- CAMBANIS , S. and MASRY , E. 1994 . Wavelet approximation of deterministic and random signals: convergence properties and rates . IEEE Transactions on Information Theory. , 40 : 1013 – 1029 .
- CHEN , H. W. 1995 . Modeling and identification of parallel non-linear systems: structural classification and parameter estimation methods . Proceedings of the IEEE , 83 : 39 – 66 .
- DAUBECHIES , I. 1992 . Ten Lectures on Wavelets , Philadelphia : SIAM .
- DELYON , B. and JUDITSKY , A. 1995 . “ Estimating wavelet coefficients ” . In Wavelets and Statistics , Edited by: Antoniadis , A. and Oppenheim , G. 151 – 168 . Berlin : Springer .
- DOYLE , F. J. , PEARSON , R. K. and OGUNNAIKE , B. A. 2002 . Identification and Control Using Volterra Models , London : Springer .
- ESKINAT , E. , JOHNSON , S. H. and LUYBEN , W. L. 1991 . UseHammerstein models in identification of non-linear systems . American Institute of Chemical Engineering , 37 : 255 – 268 .
- FENG , W. Y. , GENCELI , H. and NIKOLAOU , M. 1996 . Constrained model predictive control with simultaneous identification using wavelets . Computers and Chemical Engineering. , 20 : 1011 – 1016 .
- GIANNAKIS , G. B. and SERPEDIN , E. 2001 . A bibliography on nonlinear system identification . Signal Processing. , 81 : 533 – 580 .
- GIUNTA , B. , JACOVITTI , G. and NERI , A. 1991 . Bandpass non-linear system identification by higher cross correlation . IEEE Transactions on Signal Processing , 29 : 2092 – 2095 .
- GREBLICKI , W. 1989 . Nonparametric orthogonal series identification of Hammerstein systems . International Journal of Systems Science. , 20 : 2355 – 2367 .
- GREBLICKI , W. 1992 . Nonparametric identification of Wiener systems . IEEE Transactions on Information Theory , 38 : 1487 – 1493 .
- GREBLICKI , W. and PAWLAK , M. 1986 . Identification of discrete Hammerstein system using kernel regression estimates . IEEE Transactions on Automatic Control , 31 : 74 – 77 .
- GREBLICKI , W. 1994 . Nonparametric identification of Wiener systems by orthogonal series . IEEE Transactions on Automatic Control. , 39 : 2077 – 2086 .
- GREBLICKI , W. and KRZYZAK , A. 1979 . Nonparametric identification of a memoryless system with a cascade structure . International Journal of Systems Science , 10 : 1301 – 1310 .
- GREBLICKI , W. and PAWLAK , M. 1985 . Fourier and Hermite series estimates of regression function . Annals of The Institute of Statistical Mathematics. , 37 : 443 – 455 .
- GREBLICKI , W. and PAWLAK , M. 1987 . Hammerstein system identification by non-parametric regression estimation . International Journal of Control , 45 : 343 – 354 .
- GREBLICKI , W. and PAWLAK , M. 1991 . Nonparametric identification of a cascade nonlinear time series system . Signal Processing , 22 : 61 – 75 .
- GREBLICKI , W. and PAWLAK , M. 1994a . Cascade non-linear system identification by a non-parametric method . International Journal of Systems Science , 25 : 129 – 153 .
- GREBLICKI , W. and PAWLAK , M. 1994b . Nonparametric recovering nonlinearities in block oriented systems with the help of Laguerre polynomials . Control-Theory and Advanced Technology , 10 : 771 – 791 .
- GREBLICKI , W. and PAWLAK , M. 1994c . Dynamic system identification with order statistics . IEEE Transactions on Information Theory. , 40 : 1474 – 1489 .
- HABER , R. and KEVICZKY , L. 1999 . Nonlinear System Identification: Input-Output Modeling Approach , Dordrecht : Kluwer .
- HANNAN , E. J. and DEISTLER , M. 1988 . The Statistical Theory of Linear Systems , New York : Wiley .
- HÄRDLE , W. , KERKYACHARIAN , G. , PICARD , D. and TSYBAKOV , A. 1998 . Wavelets. Approximation, and Statistical Applications , Berlin : Springer .
- HASIEWICZ , Z. 1987 . Identifiability of large-scale interconnected linear zero-memory systems . International Journal of Systems Science. , 18 : 649 – 664 .
- HASIEWICZ , Z. 1988a . Two-stage procedure for parameter estimation in large-scale interconnected linear zero-memory systems . International Journal of Systems Science , 19 : 497 – 516 .
- HASIEWICZ , Z. 1988b . Identifiability analysis of interconnected zeromemory composite systems . International Journal of Systems Science , 19 : 1731 – 1749 .
- HASIEWICZ , Z. 1989 . Applicability of least-squares to the parameter estimation of large-scale no-memory linear composite systems . International Journal of Systems Science , 20 : 2427 – 2449 .
- HASIEWICZ , Z. 1999 . Hammerstein system identification by the Haar multiresolution approximation . International Journal of Adaptive Control and Signal Processing. , 13 : 691 – 717 .
- HASIEWICZ , Z. 2001 . Non-parametric estimation of non-linearity in a cascade time series system by multiscale approximation . Signal Processing , 81 : 791 – 807 .
- HUNTER , I. W. and KORENBERG , M. J. 1986 . The identification of non-linear biological systems: Wiener and Hammerstein cascade models . Biological Cybernetics , SS : 135 – 144 .
- JANG , W. and KIM , G. 1994 . Identification of loudspeaker non-linearities using the NARMAX modelling technique . Journal of Audio Engineering Society , 42 : 50 – 59 .
- JANSEN , M. 2001 . Noise Reduction by Wavelet Thresholding , new York : Springer .
- JUDITSKY , A. , HJALMARSSON , H. , BENVENISTE , A. , DELYON , B. , LJUNG , L. , SJOBERG , J. and ZHANG , Q. H. 1995 . Nonlinear black-box models in system-identification-mathematical foundations . Automatica. , 31 : 1725 – 1750 .
- KITADA , Y. 1998 . Identification of nonlinear structural dynamic systems using wavelets . Journal of Engineering Mechanics-ASCE. , 124 : 1059 – 1066 .
- KRZYZAK , A. 1989 . Identification of discrete Hammerstein systems by the Fourier series regression estimate . International Journal of Systems Science , 20 : 1729 – 1744 .
- KWAK , B. J. , YAGLE , A. E. and LEVITT , J. A. Non-linear system identification of hydraulic actuator. Friction dynamics using a Hammerstein model . Proceedings IEEE International Conference on Acoustics. Speech and Signal Processing ICASSP'98 . Vol. 4 , pp. 1933 – 1936 .
- MALLAT , S. G. 1998 . A Wavelet Tour of Signal Processing , San Diego : Academic Press .
- MARMARELIS , P. Z. and NAHA , U. I. 1974 . Identification of biological systems . IEEE Transactions on Biomedical Engineering. , 21 : 88 – 101 .
- PAWLAK , M. 1991 . On the series expansion approach to the identification of Hammerstein systems . IEEE Transactions on Automatic Control. , 36 : 763 – 767 .
- PAWLAK , M. and HASIEWICZ , Z. 1998 . Nonlinear system identification by the Haar multiresolution analysis . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. , 45 : 945 – 961 .
- RAFAJLOWICZ , E. 1987 . Nonparametric orthogonal series estimators of regression: A class attaining the optimal convergence rate in L2 . Statistic and Probability Letters. , 5 : 219 – 224 .
- SCOTT , D. W. 1992 . Mulfivariate Density Estimation. Theory. Practice, and Visualization , New York : Wiley .
- SJOBERG , J. , ZHANG , Q. H. , LJUNG , L. , BENVENISTE , A. , DELYON , B. , GLORENEC , P. Y. , HJALMARSSON , H. and JUDITSKY , A. 1995 . Nonlinear black-box modeling in system-identification-a unified overview . Automatica. , 31 : 1691 – 1724 .
- STONE , C. J. 1982 . Optimal global rates of convergence for nonparametric regression . Annals of Statistics. , 10 : 1040 – 1053 .
- SURESHBABU , N. and FARRELL , J. A. 1999 . Wavelet based system identification for non-linear control . IEEE Transactions on Automatic Control. , 44 : 412 – 417 .
- SLIWINSKI , P. 2000 . Non-linear system identification using wavelet algorithms , Wroclaw : Institute of Engineering Cybernetics, Wroclaw University of Technology . PhD thesis
- VÖRÖS , J. 1999 . Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities . IEEE Transactions on Automatic Control. , 44 : 2145 – 2149 .
- WALLEN , A. 2000 . Tools for Autonomous Process Control , Lund : Wallin-Dalholm .
- WANG , J. , WANG , D. , MOORE , P. and Pu , J. 2001 . Modelling study, analysis and robust servo control of pneumatic cylinder actuator systems . IEE Proceedings: Control Theory and Applications. , 148 : 35 – 42 .
Identification of non-linear characteristics of a class of block-oriented non-linear systems via Daubechies wavelet-based models
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