Analysis of the frequency response function for linear and quadratic non-linear systems using vector notation

Abstract

We have attempted to express the frequency response functions of a linear and a quadratic non-linear system in terms of spectral vectors. These vector notations convey the system characteristics in physically realisable measures. One of the valuable tools to verify the non-linear system features is the expression of a coherence function using vector notation. The visualisation of a coherence function demonstrates the dependency of an output signal on the linear and quadratic non-linear terms in the Volterra model. Multiple coherence functions are also introduced to validate the modelling errors. (C) 2003 Elsevier Science Ltd. All rights reserved.