Non-linear systems in the frequency domain: Energy transfer filters

References

• AMOS , S. W. 1977 . Radio, TV, and Technical Reference Book , Newnes-Butterworths .
   Google Scholar
• BAKER , G. L. and GOLLUB , J. P. 1990 . Chaotic Dynamics: an Introduction , Cambridge , , UK : Cambridge University Press .
   Google Scholar
• BILLINGS , S. A. and CHEN , S. 1989 . Extended model set, global data and threshold model identification of severely nonlinear systems . International Journal of Control , 50 : 1897 – 1923 .
   Web of Science ®Google Scholar
• BILLINGS , S. A. and PEYTON-JONES , J. C. 1990 . Mapping nonlinear integro-differential equation into the frequency domain . International Journal of Control , 54 : 863 – 879 .
   Web of Science ®Google Scholar
• BOYD , S. and CHUA , L. O. 1985 . Fading memory and the problem of approximating nonlinear operators with Volterra series . IEEE Transactions on Circuits and Systems , 32 : 1150 – 1161 .
   Google Scholar
• CHEN , S. and BILLINGS , S. A. 1989 . Representation of nonlinear systems: the NARMAX model . International Journal of Control , 49 : 1013 – 1032 .
   Web of Science ®Google Scholar
• DENNIS , J. E. and SCHNABEL , R. B. 1983 . Numerical Methods for Unconstrained Optimization and Nonlinear Equations , Englewood Cliffs , NJ : Prentice-Hall .
   Google Scholar
• DUFFING , G. 1918 . Erzwungene Schwingungen bei weranderlicher eigenfrequenz , Braunschweig : Vieweg .
   Google Scholar
• GEORGE , D. A. 1959 . Continuous Nonlinear Systems , Technical Report No. 335 California , , USA : MIT Research Laboratory .
   Google Scholar
• HAYKIN , S. S. 1933 . Communication Systems , New York : Wiley .
   Google Scholar
• HEREDIA , E. A. and ARCE , G. R. 2000 . Nonlinear filters based on combinations of piecewise polynomials with compact support . IEEE Transactions on Signal Processing , 48 : 2850 – 2863 .
   Web of Science ®Google Scholar
• HIRSCH , M. W. and SMALE , S. 1974 . Differential Equations, Dynamical Systems, and Linear Algebra , New York : Academic Press .
   Google Scholar
• KIM , K. I. and POWERS , E. J. 1988 . A digital method of modelling quadratically nonlinear systems with a general random output . IEEE Transactions on Acoustics, Speech, Signal Processing , 36 : 1758 – 1769 .
   Google Scholar
• KOTSIOS , S. 1997 . Finite input/output representative of a class of Volterra polynomial systems . Automatica , 33 : 257 – 262 .
   Web of Science ®Google Scholar
• KOTSIOS , S. and KALOUPTSIDIS , N. 1993 . The model matching problem for a certain class of nonlinear systems . International journal of Control , 57 : 881 – 919 .
   Web of Science ®Google Scholar
• LANG , Z.-Q. and BILLINGS , S. A. 1996 . Output frequency characteristics of nonlinear systems . International Journal of Control , 64 : 1049 – 1067 .
   Web of Science ®Google Scholar
• LANG , Z.-Q. and BILLINGS , S. A. 1997 . Output frequencies of nonlinear systems . International Journal of Control , 67 : 713 – 730 .
   Web of Science ®Google Scholar
• LEONTARITB , I. J. and BILLINGS , S. A. 1935 . input-output parametric models for nonlinear systems. Part I: Deterministic nonlinear systems . International Journal of Control , 41 : 329 – 344 .
   Web of Science ®Google Scholar
• MATHEWS , V. J. 1991 . Adaptive polynomial filters . IEEE Signal Processing Magazine , : 10 – 20 .
   Web of Science ®Google Scholar
• MATHEWS , V. J. and SICURANZA , L. G. 2000 . Polynomial Signal Processing , New York : Wiley .
   Google Scholar
• MATSUMOTO , T. , KOMURO , M. , KOKUBU , H. and TOKUNAGA , R. 1993 . Bifurcations: Sights, Sounds and Mathematics , Tokyo : Springer-Verlag .
   Google Scholar
• NAM , S. W. and POWERS , E.j. 1994 . Application of higher order spectral analysis to cubicaly nonlinear system identification . IEEE Transactions on Signal Processing , 42 : 1746 – 1765 .
   Web of Science ®Google Scholar
• NAUCK , D. , KLAWONN , F. and KRUSE , R. 1997 . Foundations of Neuro-Fuzzy Systems , Chichester , , UK : Wiley .
   Google Scholar
• PEARSON , R. K. 1999 . Discrete Time Dynamics Models , Oxford University Press .
   Google Scholar
• PEYTON-JONES , J. C. and BILLINGS , S. A. 1989 . A recursive algorithm for computing the frequency response of a class of nonlinear difference equation models . International Journal of Control , 50 : 1925 – 1940 .
   Web of Science ®Google Scholar
• PEYTON-JONES , J.C. and BILLINGS , S. A. 1990 . Interpretation of nonlinear frequency response functions . International Journal of Control , 62 : 319 – 346 .
   Web of Science ®Google Scholar
• POPOVIC , P. N. , ALI , H. , KYOYAL , H and NAYFEH , S. A. 1995 . An experimental investigation of energy transfer from a high frequency mode to a low frequency mode in a flexible structure . Journal of Vibration and Control , 1 : 115 – 128 .
   Google Scholar
• RAZ , G. M. and VAN VEEN , B. D. 1998 . Baseband Volterra filters for implementing carrier based nonlinearities . IEEE Transactions on Signal Processing , 46 : 103 – 114 .
   Web of Science ®Google Scholar
• RUGH , W. J. 1981 . Nonlinear System Theory: the Volterra/ Wiener Approach , Baltimore , MD : The Johns Hopkins University Press .
   Google Scholar
• SCHETZEN , M. 1980 . The Volterra and Wiener Theories of Nonlinear Systems , New York : Wiley .
   Google Scholar
• SICURANZA , G. L. 1992 . Quadratic filters for signal processing . Proceedings of the IEEE , 80 : 1263 – 1285 .
   Web of Science ®Google Scholar
• SZCZEPANSKI , S. and SCHAUMANN , R. Effects of weak nonlinearities in transconductance capacitor filters . Proceedings of the IEEE International Symposium on Circuits and Systems . pp. 1055 – 1058 .
   Google Scholar
• SZCZEPANSKI , S. and SCHAUMANN , R. 1933 . Nonlinearityinduced distortion of the transfer function shape in highorder OTA-C filters . Analogue Integrated Circuits and Signal Processing , 3 : 143 – 151 .
   Web of Science ®Google Scholar
• TICK , L. J. 1951 . f The estimation of transfer functions of quadratic systems . Technomics , 3 : 503 – 507 .
   Google Scholar
• ZELNIKER , G. and TAYLOR , F. J. 1994 . Advanced Digital Signal Processing: Theory and Applications , New York : Marcel Dekker .
   Google Scholar