Editing Causal system (section)

== Mathematical definitions ==

Definition 1: A system mapping <math>x</math> to <math>y</math> is causal if and only if, for any pair of input signals <math>x_{1}(t)</math>, <math>x_{2}(t)</math> and any choice of <math>t_{0}</math>, such that
:<math>x_{1}(t) = x_{2}(t), \quad \forall \ t < t_{0},</math>
the corresponding outputs satisfy
:<math>y_{1}(t) = y_{2}(t), \quad \forall \ t < t_{0}.</math>

Definition 2: Suppose <math>h(t)</math> is the impulse response of any system <math>H</math> described by a linear constant coefficient differential equation. The system <math>H</math> is causal if and only if
:<math>h(t) = 0, \quad \forall \ t <0 </math>
otherwise it is non-causal.