An asymptotic causality requirement for systems with constrained inputs

Abstract

The usual formulation of causality for simple linear systems: “no output before input”, may fail to imply that the system kernel K( τ) is a causal function of the time delay τ, because the class of physically admissible input functions may not contain a complete set of causal signals. An attempt is made to formulate a causality requirement, asymptotic in nature, which overcomes this difficulty. It is found, rather generally, that systems which satisfy this requirement cannot have a finitely acausal kernel. If it could be shown that the kernel cannot be infinitely acausal, the validity of the usual dispersion relations for such systems would be ensured.