New results on the generalized frequency response functions of nonlinear volterra systems described by NARX model

In order that the nth-order Generalized Frequency Response Function (GFRF) for nonlinear systems described by a NARX model can be directly written into a more straightforward and meaningful form in terms of the first order GFRF and model parameters, the nth-order GFRF is now determined by a new mapping function based on a parametric characteristic. This can explicitly unveil the linear and nonlinear factors included in the GFRFs, reveal clearly the relationship between the nth-order GFRF and the model parameters, and also the relationship between the nth-order GFRF and the first order GFRF. Some new properties of the GFRFs can consequently be developed. These new results provide a novel and useful insight into the frequency domain analysis of nonlinear systems.