Iterative method for the definition of frequency-domain volterra models

The interest towards nonlinear system modeling and identification is growing in the last years since more and more often the usual linear time invariant approach is not able to satisfy the requirements in terms of accuracy. Among the several types of nonlinear models, the Volterra series represents a very effective tool, being the straightforward generalization of the conventional approach. However, the number of coefficients grows exponentially with the order of nonlinearity to be considered. Therefore, in common applications, only low-order Volterra models are employed. Nowadays, the increase of computational power makes possible to employ frequency-domain Volterra models having a nonlinearity order higher than two or three, but a procedure allowing to write the frequency-domain kernels in a simple way has not been developed yet. The purpose of this work is to present an iterative method that allows writing the generic expression of frequency domain Volterra models considering a generic number of input harmonics and order of nonlinearity.