Identification of Volterra Models of Tube Audio Devices using Multiple-Variance Method

The multiple-variance method is a cross-correlation method that exploits input signals with different powers for the identification of a nonlinear system by means of the Volterra series. It overcomes the problem of the locality of the solution of traditional nonlinear identification methods, based on mean square error minimization or cross-correlation, that well approximate the system only for inputs that have approximately the same power of the identification signal. The multiple-variance method permits to improve the performance of models of systems that have inputs with high dynamic, like audio amplifiers. This method is used, for the first time, to identify three different tube amplifiers. The method is applied to a novel reduced Volterra model that allows to overcome the problem of the very large number of coefficients required by the Volterra series by choosing only a proper subset of elements from each kernel. Eventually, the multiple-variance methodology is applied to different real audio tube devices demonstrating the effectiveness of the proposed approach in terms of system identification and computational complexity.