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

By Tokunbo Ogunfunmi

ISBN-10: 0387263284

ISBN-13: 9780387263281

ISBN-10: 0387686304

ISBN-13: 9780387686301

Makes a speciality of method identity functions of the adaptive tools provided. yet that could even be utilized to different functions of adaptive nonlinear methods. Covers contemporary learn leads to the world of adaptive nonlinear method id from the authors and different researchers within the box.

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

Example text

The solutions of the Hermite’s differential equation are referred to as Hermite polynomials, H n ( x) . Hermite polynomials H n ( x) can be expressed as (Efunda 2006): H n ( x) = (−1) n e x 2 d n − x2 (e ) where n = 0,1, 2,3...... dx n 34 Chapter 2 The generating function of the Hermite polynomial is ∞ H n ( x)t n n! n=0 e 2tx−t = ∑ 2 It can be shown that ∞ ∫e −∞ − x2 ⎧⎪0, m ≠ n H m ( x) H n ( x)dx = ⎨ n ⎪⎩2 n ! π m = n We note that H n ( x) is even when n is even and H n ( x) is odd when n is odd.

The output yi (or y (n) ) is represented by a weighted sum of monomials of input signal xi (or x(n) ). If y (n) = f ( x(n)) , then we have an example such as: 32 Chapter 2 Q f ( x(n)) = ∑ c ( q ) x q (n) q =0 f ( x(n)) = c (0) + c x(n) + c x (n) + c (3) x3 (n) + ....... 16) q =0 where the notation M ( q ) ( x) = x q is introduced to represent polynomial powers and x(n) has been replaced by just x . 4. The matrix X is defined as the matrix with N (# of data inputs) rows and Q=q+1 (# of parameters) columns.

For non-negative n = 0,1, 2, 3,........ , the solutions of the Hermite’s differential equation are referred to as Hermite polynomials, H n ( x) . Hermite polynomials H n ( x) can be expressed as (Efunda 2006): H n ( x) = (−1) n e x 2 d n − x2 (e ) where n = 0,1, 2,3...... dx n 34 Chapter 2 The generating function of the Hermite polynomial is ∞ H n ( x)t n n! n=0 e 2tx−t = ∑ 2 It can be shown that ∞ ∫e −∞ − x2 ⎧⎪0, m ≠ n H m ( x) H n ( x)dx = ⎨ n ⎪⎩2 n ! π m = n We note that H n ( x) is even when n is even and H n ( x) is odd when n is odd.

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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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