## Adaptive nonlinear system identification: the Volterra and Wiener model approachesAdaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches introduces engineers and researchers to the field of nonlinear adaptive system identification. The book includes recent research results in the area of adaptive nonlinear system identification and presents simple, concise, easy-to-understand methods for identifying nonlinear systems. These methods use adaptive filter algorithms that are well known for linear systems identification. They are applicable for nonlinear systems that can be efficiently modeled by polynomials. After a brief introduction to nonlinear systems and to adaptive system identification, the author presents the discrete Volterra model approach. This is followed by an explanation of the Wiener model approach. Adaptive algorithms using both models are developed. The performance of the two methods are then compared to determine which model performs better for system identification applications. Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches is useful to graduates students, engineers and researchers in the areas of nonlinear systems, control, biomedical systems and in adaptive signal processing. |

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### Contents

Introduction to Nonlinear Systems | 1 |

Polynomial Models of Nonlinear Systems | 19 |

Volterra and Wiener Nonlinear Models | 39 |

Copyright | |

10 other sections not shown

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### Common terms and phrases

adaptive algorithm adaptive filter adaptive system identification applied autocorrelation matrix bilinear chapter computational complexity convergence cost function defined desired response differential equation discrete nonlinear Wiener discrete Wiener model discrete-time eigenvalue spread estimate example filter coefficients G-functional Gm[km gradient Hermite polynomials homogeneous homogeneous functional identity matrix implementation impulse response infinite impulse response input vector input x(n inverse QR ISBN kernel coefficients learning curve least squares linear systems LMS algorithm mean square error misadjustment neural network nonlinear adaptive system nonlinear systems nonlinear Wiener model Note ns(n optimization optimum order Volterra orthogonal orthonormal parameter polynomial models properties Q-polynomial QR decomposition quadratic representation RLS-type second-order Volterra shown in figure signal processing simulation solution subset selection Substituting equation Theoretical value time-invariant truncated Volterra series update variance Volterra and Wiener Volterra filter Volterra functional Volterra kernel Volterra model Volterra series Volterra series model Volterra system weight vector Wiener filter Wiener kernel zero mean