A behavioral equation framework for time-domain transmissibilities

Transmissibilities are widely used in engineering to express the relationship between sets of signals that are not necessarily inputs and outputs in the usual causal sense. Despite their usefulness, a rigorous intellectual framework for transmissibilities has been lacking. In this paper we demonstrate that behavioral equations provide a suitable framework for time-domain transmissibilities by choosing the latent variables in the behavioral equations to be the external signals that drive the system. This connection provides a theoretical foundation for time-domain transmissibilities and demonstrates the relevance of behavioral modeling to an important class of applications.