A comparative overview of frequency domain methods for nonlinear systems

The widespread acceptance of frequency domain techniques for linear and time invariant systems has been an impetus for the extension of these methodologies toward nonlinear systems. However, differences and equivalences between alternative methods have been less addressed. This paper provides a comparative overview of four classes of frequency domain methods for nonlinear systems: Volterra based models, nonlinear frequency response functions / Bode plots, describing functions and linear approximations in the presence of nonlinearities. Each method is introduced using consistent nomenclature and terminology, which allows for comparison in terms of system and signal classes for which the methods are valid as well as the type of (nonlinear) effects captured by each model. Summarizing, the paper aims to connect, and make different frequency domain methods for nonlinear systems accessible, by providing a comparative overview of such methodologies, accompanied by illustrative (experimental) examples.