A semi-parametric polynomial frequency response estimator for identification of weakly non-linear systems using multi-amplitude MLS measurements

In this article a method for the measurement of the linear frequency response of weakly non-linear systems is described. A frequency domain estimator is developed by analyzing the output spectra for single- and multitone excitations of several types of system models with the most complex system one being a parallel-cascade Wiener-Hammerstein-type model which is able to represent a wide range of weakly non-linear systems. It is then shown that the output spectrum of such a weakly non-linear system can be expressed by a polynomial with constant coefficients for a given input signal at each frequency. This leads to the proposed polynomial estimator Hp that is capable of identifying the true linear, nonparametric frequency response of the system under test. Special versions for either input or output noise only are developed and consistency is shown for all considered system models.