Before revision: Mathematical definitions Definition 1: A system mapping to is causal if and only if, for any pair of input signals and such that the corresponding outputs satisfy Definition 2: Suppose is the impulse response of any system described by a linear constant coefficient differential equation.
After revision: Mathematical definitions Definition 1: A system mapping to is causal if , and any choice of , only if, for any pair of input signals and such that the corresponding outputs satisfy Definition 2: Suppose is the impulse response of any system described by a linear constant coefficient differential equation.