PARAMETRIC AND NONPARAMETRIC IDENTIFICATION OF LINEAR-SYSTEMS IN THE PRESENCE OF NONLINEAR DISTORTIONS - A FREQUENCY-DOMAIN APPROACH

This paper studies the asymptotic behavior of nonparametric and parame tric frequency domain identification methods to model linear dynamic s ystems in the presence of nonlinear distortions under some general con ditions for random multisine excitations, In the first part, a related linear dynamic system (RLDS) approximation to the nonlinear system (N LS) is defined, and it is shown that the differences between the NLS a nd the RLDS can be modeled as stochastic variables with known properti es, In the second part a parametric model for the RLDS is identified, Convergence in probability of this model to the RLDS is proven, A func tion of dependency is defined to detect and separate the presence of u nmodeled dynamics and nonlinear distortions and to hound the bias erro r on the transfer function estimate.