Journal ArticleDOI
Identifying nonlinear difference equation and functional expansion representations : the fast orthogonal algorithm
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A method is presented for identifying functional expansion and difference equation representations for nonlinear systems which greatly reduces computing time, so that 15-fold increases in speed of estimating kernels or difference equation coefficients are readily obtainable, compared with a previous orthogonal technique.Abstract:
A method is presented for identifying functional expansion and difference equation representations for nonlinear systems. The method relies on an orthogonal approach which does not require explicit creation of orthogonal functions. This greatly reduces computing time, so that 15-fold increases in speed of estimating kernels or difference equation coefficients are readily obtainable, compared with a previous orthogonal technique. In addition, storage requirements are considerably diminished. A wide variety of input excitation, both random and deterministic, can be used, and the method is not limited to inputs which are Gaussian, white or lengthy. A model of the peripheral auditory system is simulated to show kernel measurement is free of artifacts using the present method, in contrast to the crosscorrelation approach.read more
Citations
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Adaptive polynomial filters
TL;DR: The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion or a recursive nonlinear difference equation.
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Identification of nonlinear biological systems using Laguerre expansions of kernels.
TL;DR: Another implementation of the Volterra-Wiener kernel estimation technique is presented, which utilizes least-squares fitting instead of covariance time-averaging and provides for the proper selection of the intrinsic Laguerre parameter “α”.
Journal ArticleDOI
A bibliography on nonlinear system identification
TL;DR: The present bibliography represents a comprehensive list of references on nonlinear system identification and its applications in signal processing, communications, and biomedical engineering.
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Detection of nonlinear dynamics in short, noisy time series
Mauricio Barahona,Chi-Sang Poon +1 more
TL;DR: A computational procedure is presented, based on a comparison of the prediction power of linear and nonlinear models of the Volterra–Wiener form, which is capable of robust and highly sensitive statistical detection of deterministic dynamics, including chaotic dynamics, in experimental time series.
Journal ArticleDOI
Model selection approaches for non-linear system identification: a review
TL;DR: A systematic overview of basic research on model selection approaches for linear-in-the-parameter models, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design is presented.
References
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Book
Nonlinear Problems in Random Theory
Norbert Wiener,T. Teichmann +1 more
TL;DR: A series of lectures on the role of nonlinear processes in physics, mathematics, electrical engineering, physiology, and communication theory was given in this article, where the last few of these were devoted to the application of my ideas to problems in the statistical mechanics of gases.
Journal ArticleDOI
Input-output parametric models for non-linear systems Part II: stochastic non-linear systems
TL;DR: Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined.
Journal ArticleDOI
The identification of nonlinear biological systems: Wiener and Hammerstein cascade models
W I Hunter,Michael J. Korenberg +1 more
TL;DR: Various identification schemes that have been proposed for the Hammerstein and Wiener systems are critically reviewed with reference to the special problems that arise in the identification of nonlinear biological systems.
Journal ArticleDOI
Measurement of the Wiener Kernels of a Non-linear System by Cross-correlation†
Y. W. Lee,M. Schetzen +1 more
TL;DR: In this article, a practical and relatively simple method of measuring the Wiener kernels of a non-linear system is presented, which is based upon cross-correlation techniques and avoids orthogonal expansions such as those of the original Wiener method of measurement.
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Measurement of the Wiener Kernels of a Non-linear System by Cross-correlation†
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