An explicit mapping between the frequency domain and the time domain representations of nonlinear systems

摘要

Explicit expressions are presented that describe the input-output behaviourof a nonlinear system in both the frequency and the time domain. Theexpressions are based on a set of coefficients that do not depend on the inputto the system and are universal for a given system. The anharmonic oscillatoris chosen as an example and is discussed for different choices of its physicalparameters. It is shown that the typical approach for the determination of theVolterra Series representation is not valid for the important case when thenonlinear system exhibits oscillatory behaviour and the input has a pole at theorigin (in the frequency domain), e.g. the unit-step function. For this case,resonant effects arise and the analysis requires additional care.