Extending the transfer function calculus of time-varying linear systems: a generalized underspread theory

We extend the approximate transfer function calculus of "underspread" linear time-varying (LTV) systems introduced by W. Kozek (1992). Our extension is based on a new, generalized definition of underspread LTV systems that does not assume finite support of the systems' spreading function. We establish explicit bounds on various error quantities associated with the transfer function approximation. Our results yield a simple and convenient transfer function calculus for a significantly wider and practically more relevant class of LTV systems than that previously considered.