Frequency Domain Kernel Estimation for 2nd-order Volterra Models Using Random Multi-tone Excitation

We consider the problem of frequency domain kernel estimation using random multi-tone (harmonic) excitation for 2nd-order Volterra models. The basic approach is based on least squares minimization of model output error, and results for the Volterra kernel estimations with random multi-tone inputs and random Gaussian input are compared. We show that kernel estimation with multi-tones are very accurate and efficient compared to the latter. As an illustration, the proposed method is applied to a discrete input–output system obtained from the numerical simulation of a representative hydrodynamic system for modeling semiconductor device transport. We also consider the effect of noise in the kernel estimation.