By Tokunbo Ogunfunmi

ISBN-10: 0387263284

ISBN-13: 9780387263281

ISBN-10: 0387686304

ISBN-13: 9780387686301

Specializes in approach identity purposes of the adaptive equipment offered. yet that could even be utilized to different purposes of adaptive nonlinear methods. Covers fresh study ends up in the world of adaptive nonlinear approach id from the authors and different researchers within the box.

**Read Online or Download Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches (Signals and Communication Technology) PDF**

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**Extra info for Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches (Signals and Communication Technology)**

**Sample text**

More extensions and variations of nonlinear orthogonal Wiener models will be developed in the next few chapters. 1 Nonorthogonal Polynomial Models A polynomial nonlinear system can be modeled by the sum of increasing powers of the input signal, x(n). In general, the positive powers of x(n) are x ( n), x 2 ( n), x 3 (n), x 4 (n), x 5 (n),...... Let x(n) and y(n) represent the input and output signals, respectively. For a linear causal system, the output signal y(n) can be expanded as the linear combination of M-memory input signal x(n) as y(n) = c0x(n) + c1x(n-1) + c2x(n-2) + c3x(n-3) + ...

The particular polynomials to be used are determined by the characteristics of the input signal that we are required to model. For Gaussian, white input, the Hermite polynomials are chosen. We note that the set of Hermite polynomials is an orthogonal set in a statistical sense. This means that the Volterra series can be represented by some linear combination of Hermite polynomials. In fact every Volterra series has a unique Wiener model representation. This model gives us a good eigenvalue spread of autocorrelation matrix (which is a requirement for convergence of gradient-based adaptive filters as discussed in chapter 5), and also allows us to represent a complicated Volterra series without over-parameterization with only a few coefficients.

For Gaussian, white input, the Hermite polynomials are chosen. We note that the set of Hermite polynomials is an orthogonal set in a statistical sense. This means that the Volterra series can be represented by some linear combination of Hermite polynomials. In fact every Volterra series has a unique Wiener model representation. This model gives us a good eigenvalue spread of autocorrelation matrix (which is a requirement for convergence of gradient-based adaptive filters as discussed in chapter 5), and also allows us to represent a complicated Volterra series without over-parameterization with only a few coefficients.

### Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches (Signals and Communication Technology) by Tokunbo Ogunfunmi

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