Definition of Pruned Frequency-Domain Volterra Models Based on Knowledge About the Input Spectrum

The Volterra representation is one of the most widely employed approaches to the behavioral modeling of nonlinear time invariant systems in the frequency domain. Its main drawback is that the input-output relationship is defined by a set of coefficients, whose cardinality rapidly grows with the considered nonlinearity degree and with the number of input harmonics. The purpose of this work is proposing a method that, assuming to know which are the strongest spectral components in the typical input signals, allows writing a subclass of Volterra models whose behaviors are defined by a dramatically lower number of coefficients, with minor impact on accuracy. According to this information, input spectral components are classified into large, small and linear. The output spectrum is computed by considering all the possible interactions between large components, as from the Volterra theory. On the contrary, small components interact only with large components, but not with each other. Linear components are linearly transferred to the output. The effectiveness of the pruning technique is evaluated with both numerical simulations and experiments. Results highlight the advantages and the flexibility enabled by the proposed approach, which become even more evident in the presence of significant noise during identification.