In this study, recent advances in higher-order spectral analysis techniques and Volterra system theory have been utilized to yield a practical tool for the identification of weakly nonlinear systems up to third order. The emphasis is on the frequency-domain analysis of the system input-output data because of the insight it gives us into a very powerful technique, i.e., nonlinear transfer function (NTF) approach. The NTF approach is general and practical in that (i) it can handle various types of nonlinear systems (i.e., systems which can be described by a Volterra series up to third-order), and (ii) a wide variety of input excitations (including Gaussian and nonGaussian) can be utilized for the system identification.;A matrix formulation for the system I/O representation is presented. Next, a description of the identification techniques and their digital implementations, which employ the well-known linear solution techniques, e.g., the Cholesky method and a RLS adaptive algorithm, are given in detail. Furthermore, experimental knowledge of the system transfer functions is utilized to (i) solve the spectral decomposition problem, (ii) compute the generalized system coherency functions, which provide a goodness-of-fit measure for the validity of the Volterra model, (iii) estimate the system parameters that appear in many nonlinear system equations, and (iv) reduce unwanted nonlinear effects or linearize a given Volterra system. Also, an efficient and fast algorithm for the classification of the third-order intermodulation and harmonic products is presented, which utilizes the analysis results derived for the NTF approach.
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