A pruning technique for volterra models: Exploiting knowledge about input spectrum

Behavioral modeling and identification of nonlinear time invariant systems in the frequency domain represents an extremely interesting and up to date topic in widespread application fields. The frequency-domain Volterra-Wiener (or polynomial) approach is one of the most widely employed, since it can be derived as the straightforward extension of the usual frequency response function to the nonlinear case. Its main drawback is that its complexity rapidly grows with the number of input harmonic components and nonlinearity order. The purpose of this work is presenting a method to reduce the number of coefficients defining the Volterra models by exploiting a priori knowledge about the input signal spectral content. Similarly to the spectral linearization approximation which is commonly used in radiofrequency and microwave applications, input components are classified into "large" and "small" according to their expected amplitudes. The output spectrum is computed by considering all the possible interactions between large components according to the Volterra theory. On the contrary, interactions between small components are neglected. The proposed modeling approach has been tested in numerical simulations on a Hammerstein system; results clearly show the advantages with respect to a conventional polynomial model.