Measuring a linear approximation to weakly nonlinear MIMO systems

The paper addresses the problem of preserving the same LTI approximation of a nonlinear MIMO (multiple-input multiple-output) system. It is shown that when a nonlinear MIMO system is modeled by a multidimensional Volterra series, periodic noise and random multisines are equivalent excitations to the classical Gaussian noise, in a sense that they yield in the limit, as the number of the harmonics M -> infinity, the same linear approximation to the nonlinear MIMO system. This result extends previous results derived for nonlinear SISO (single-input single-output) systems. Based upon the analysis of the variability of the measured FRF (frequency response function) due to the presence of the nonlinearities and the randomness of the excitations, a new class of equivalent input signals is proposed, allowing for a lower variance of the nonlinear FRF measurements, while the same linear approximation is retrieved.