Causality
Definition: A system is causal if and only if the output y(t) at any given time depends on the input x(t) in present and/or past times; so $ y(a) $ depends on $ x(t) $ where $ t\le a $.
Side Note: All memoryless systems are causal.
Examples:
Causal System: $ y(t)=\frac{5t}{2}u(t-3) $
This system is causal because it has an output y(t) that depends on an input $ x(t)=\frac{5t}{2}u(t-3) $ where x(t) is zero for all values of $ t\le 0 $.
Non-Causal System: $ y(t)=\frac{e^{-2t}}{3}u(t+2) $
This system is not causal because it has an output y(t) that depends on an input $ x(t)=\frac{e^{-2t}}{3}u(t+2) $ where x(t) is not zero for all values of $ t\le 0 $. The input depends on values of time considered to be in the future => u(t+2).
-Tylor Thompson
