Homophase Signals Separation for Volterra Series Identification

Abstract

This article addresses the identification of non-linear systems represented by Volterra series. To improve the robustness of state-of-the-art estimation methods, we introduce the notion of “homophase signals”, for which a separation method is given. Those homophase signals are then used to derive a robust identification process. This prior step is similar to nonlinear homogeneous order separation, in which amplitude relations are used to separate the orders of a Volterra series, but offers a better conditioning by using phase deviations rather than amplitudes. First an academic phase-based method using complex-valued test signals is introduced for separating nonlinear orders. Second this notion of phase deviation is extended to real-valued signals, which leads to the design of the proposed homophase signals separation method. Finally, a new identification process is derived using the homophase signals. Simulations are used to highlight the benefits of the proposed identification process in comparison to the standard approach.