In this paper, we set up a framework to deal with nonlinear distortions in a linear modeling framework. The nonlinear system is replaced by a linear system plus a noise source. The properties of this representation are given and a measurement technique to extract the linear model and the noise variance is developed. Eventually, the different aspects of this approach are discussed from a measurement, an identification and a design point of view.
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Schoukens et al. (2002) studied this question.