A mixed-domain method for identification of quadratically nonlinear systems

A new mixed-domain method for identifying Volterra transfer functions of a nonlinear system, which can be represented by a second-order truncated Volterra series, is presented in this paper. This method is built on a discrete mixed-domain Volterra model derived from analyzing both discrete time- and frequency-domain Volterra models of quadratically nonlinear systems. It is shown that the conventional discrete frequency-domain Volterra model can be derived from the discrete mixed-domain Volterra model by making certain approximations. In this sense, the frequency-domain model can be considered to be a cough version of the mixed-domain model and thus cannot outperform the mixed-domain model in terms of modeling capability. In addition, the new method is shown to be able to properly identify the Volterra transfer functions even when the output of the quadratically nonlinear system is aliased. Based on this insight, a new anti-aliasing frequency-domain method, which is immune from the output aliasing problem, is developed. The superiority of these new methods over the conventional method is demonstrated by using them to analyze known quadratically nonlinear systems.