Selection of generalized orthonormal bases for second-order Volterra filters

Signal Processing

Volumn 85, Issue 12, 2005, Pages 2371-2385

  Kibangou, Alain Y ^a,b   Favier, Gérard ^a   Hassani, Moha M ^b  

^a UNIVERSITY OF NICE SOPHIA ANTIPOLIS   (France)

^b FACULTÉ DES SCIENCES SEMLALIA   (Morocco)

Author keywords

Basis selection; Generalized orthonormal basis; Identification; Nonlinear systems; Quadratic Volterra filters

Indexed keywords

COMPUTATIONAL COMPLEXITY; NONLINEAR SYSTEMS; PARAMETER ESTIMATION;

BASIS SELECTION; GENERALIZED ORTHONORMAL BASIS; IDENTIFICATION; QUADRATIC VOLTERRA FILTERS;

SIGNAL FILTERING AND PREDICTION;

EID: 27744505597     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2005.02.020     Document Type: Article

References (27)

1. S. Boyd, and L. Chua Fading memory and the problem of approximating nonlinear operators with Volterra series IEEE Trans. Circuits Systems 32 11 1985 1150 1161
2. W. Franck An efficient approximation to the quadratic Volterra filter and its application in real-time loudspeaker linearization Signal Processing 45 1 1995 97 113
3. M. Korenberg Parallel cascade identification and kernel estimation for nonlinear systems Ann. Biomed. Eng. 19 1991 429 455
4. T. Panicker, and V. Mathews Parallel-cascade realizations and approximations of truncated Volterra systems IEEE Trans. Signal Process. 46 10 1998 2829 2832
5. M. Schetzen The Volterra and Wiener Theories of Nonlinear Systems 1980 Wiley New York
6. R.J.G.B. Campello, W.C. Amaral, and G. Favier Optimal Laguerre series expansion of discrete Volterra models Proceedings of the European Control Conference (ECC) 2001 Porto Portugal 372 377
7. R. Hacioglu, and G. Williamson Reduced complexity Volterra models for nonlinear system identification Eurasip J. Appl. Signal Process. 4 2001 257 265
8. R. Malti, Représentation de systèmes discrets sur la base des filtres orthogonaux: Application à la modélisation des systèmes dynamiques mutivariables, Ph.D. Thesis, Institut National Polytechnique de Loraine (INPL), Nancy, France, 1999.
9. Y. Fu, and G. Dumont An optimum time scale for discrete Laguerre network IEEE Trans. Automat. Control 38 6 1993 934 938
10. R.J.G.B. Campello, G. Favier, and W.C. Amaral Optimal expansions of discrete-time Volterra models using Laguerre functions Proceedings of the IFAC SYSID 2003 Rotterdam The Netherlands 1844 1849
11. R.J.G.B. Campello, G. Favier, and W.C. Amaral Optimal expansions of discrete-time Volterra models using Laguerre functions Automatica 40 2004 815 822
12. A. Kibangou, G. Favier, and M. Hassani A growing approach for selecting generalized orthonormal basis functions in the context of system modelling Proceedings of the IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP'03 2003 Grado Italy
13. A. Kibangou, G. Favier, and M. Hassani Generalized orthonormal basis selection for expanding quadratic Volterra filters Proceedings of the IFAC SYSID 2003 2003 Rotterdam The Netherlands 1119 1124
14. B. Wahlberg System identification using Laguerre models IEEE Trans. Automat. Control 36 1991 551 562
15. S. Gunnarsson, and B. Wahlberg Some asymptotic results in recursive identification using Laguerre models Int. J. Adapt. Control Signal Process. 5 1991 313 333
16. G. Dumont, and Y. Fu Non-linear adaptive control via Laguerre expansion of Volterra kernels Int. J. Adapt. Control Signal Process. 7 1993 367 382
17. B. Wahlberg, and P. Mäkilä On approximation of stable linear systems using Laguerre and Kautz functions Automatica 32 5 1996 693 708
18. A.C. den Brinker, F. Benders, and T.O. e Silva Optimality conditions for truncated Kautz series IEEE Trans. Circuits Systems-II 43 2 1996 117 122
19. S. Abeysekera, and Z. Zang Optimal Laguerre filters for sigma-delta demodulator circuits Signal Processing 80 2000 205 209
20. M. Masnadi-Shirazi, and M. Ghasemi Adaptive Laguerre network realization Signal Processing 80 2000 2169 2186
21. G. Oliveira, W. Amaral, G. Favier, and G. Dumont Constrained robust predictive controller for uncertain processes modelled by orthonormal series functions Automatica 36 4 2000 563 571
22. P. Heuberger, P.V. den Hof, and O. Bosgra A generalized orthonormal basis for linear dynamical systems IEEE Trans. Automat. Control 40 3 1995 451 465
23. P. Bodin, T.E. Silva, B. Wahlberg, On the construction of orthonormal basis functions for system identification, in: Proceedings of the 13th IFAC World Congress, vol. I, San-Francisco, 1996, pp. 369-374.
24. B. Ninness, and F. Gustafsson A unifying construction of orthonormal bases for system identification IEEE Trans. Automat. Control 42 4 1997 515 521
25. T.O. e Silva Stationarity conditions for the L2 error surface of the generalized basis functions lattice filter Signal Processing 56 1997 233 253
26. G. Raz, and B. Van Veen Baseband Volterra filters for implementing carrier based nonlinearities IEEE Trans. Signal Process. 46 1 1998 103 114
27. G. Glentis, P. Koukoulas, and N. Kalouptsidis Efficient algorithms for Volterra system identification IEEE Trans. Signal Process. 47 11 1999 3042 3057