Adaptive Nonlinear System Identification: The Volterra and by Tokunbo Ogunfunmi PDF

By Tokunbo Ogunfunmi

ISBN-10: 0387263284

ISBN-13: 9780387263281

ISBN-10: 0387686304

ISBN-13: 9780387686301

Makes a speciality of method id purposes of the adaptive equipment provided. yet which could even be utilized to different functions of adaptive nonlinear tactics. Covers contemporary learn leads to the realm of adaptive nonlinear procedure id from the authors and different researchers within the box.

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

Example text

3) m (k) where al(m) are some proper constants. 4) denotes the inner product and δ (l − m) is the Dirac delta where , function. 5 is the first-order homogeneous functional, which means that Y1[cx(n)] = cY1[x(n)], where c is a constant. 5 can be expressed by the block diagram shown in figure 3-2: x(n) b0 a1(0) b1 a1(1) Y1[x(n)] # bm a1(m) Figure 3-2. 6, we conclude that a general first-order Volterra system with DC term is one for which the response to a linear combination of inputs is the same as the linear combination of the response of each individual input.

The basis function gm[x(n)] can be implemented with modularity as shown in figure 2-9, where the thin solid arrows and bold arrows represent the real data and complex data flows respectively. 8 is the statistical orthonormal basis set, which means that E{ g*i [x(n)]g j [x(n)] } = δ ij where δ ij is the Dirac delta function. ] -1 w0 c3 g0[x] Figure 2-9. 11) Then wm becomes an (N+L) × 1 vector whose components are chosen from the (M+1)N+L different combinations of discrete frequencies. )* means complex conjugate and cm are the coefficients to be adapted.

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. It is interesting to note that most of the linear properties of adaptive algorithms are still preserved. By using this nonlinear model, a detailed adaptation performance analysis can be done. Further development and discussion will be presented in the next few chapters.

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


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