Aliasing effects on estimating transfer functions of quadratically nonlinear systems

Previous methods developed for estimating transfer functions in the frequency domain with stochastic inputs failed to completely establish the link between the frequency domain estimates and the true system coefficients. By taking aliasing effects into consideration, the authors develop a robust scheme to estimate the time domain system coefficients of a discrete-time linear-quadratic system via a frequency domain method. Furthermore, the estimation errors can be greatly reduced by eliminating the time-aliasing effect. The robustness of this method has been tested as well.<<ETX>>

[1]  V. J. Mathews Adaptive polynomial filters , 1991, IEEE Signal Processing Magazine.

[2]  Taiho Koh,et al.  Second-order Volterra filtering and its application to nonlinear system identification , 1985, IEEE Trans. Acoust. Speech Signal Process..

[3]  Leon O. Chua,et al.  Measuring Volterra kernels , 1983 .

[4]  L. Chua,et al.  Frequency domain analysis of nonlinear systems: general theory , 1979 .

[5]  Miroslav Morhác A fast algorithm of nonlinear Volterra filtering , 1991, IEEE Trans. Signal Process..

[6]  E. J. Powers,et al.  Estimation of quadratically nonlinear systems with an i.i.d. input , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[7]  I. Sandberg On Volterra expansions for time-varying nonlinear systems , 1983 .

[8]  S. Fakhouri Identification of the Volterra kernels of nonlinear systems , 1980 .

[9]  D. Linebarger,et al.  Estimating transfer functions of quadratically nonlinear systems , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[10]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[11]  Stephen P. Boyd,et al.  Analytical Foundations of Volterra Series , 1984 .

[12]  D. Brillinger The identification of polynomial systems by means of higher order spectra , 1970 .

[13]  M. Tummala,et al.  Iterative algorithm for identification of third order Volterra systems , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[14]  S. B. Kim,et al.  Applications Of Digital Polyspectral Analysis To Nonlinear Systems Modeling And Nonlinear Wave Phenomena , 1989, Workshop on Higher-Order Spectral Analysis.

[15]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[16]  L. Chua,et al.  Frequency-domain analysis of nonlinear systems: formulation of transfer functions , 1979 .

[17]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[18]  Ping Zhang,et al.  An algorithm to measure high order Volterra kernels , 1990, IEEE International Symposium on Circuits and Systems.

[19]  Edward J. Powers,et al.  A digital method of modeling quadratically nonlinear systems with a general random input , 1988, IEEE Trans. Acoust. Speech Signal Process..