**Causal Signal**

A signal that does not start before t=0 is a causal signal i.e. x(t)=0, ∀ t<0.

A system is * causal or non-anticipatory* if the output at any time t

_{o}depends only on the values of the input at the present time and in the past.

**Note:** All memoryless systems are causal systems since the output responds only to the current value of the input.

**Non-Causal Signal**

A signal that starts before t=0 is a non-causal signal.

**Anti-Causal Signal**

A signal that ends before t=0 is an anti-causal signal i.e. x(t)=0, ∀ t>0.

**Note:** Any signal x(t) that does not contain any singularities (a delta function or its derivative) at t=0 can be written as the sum of a causal part x^{+}(t) and anti-causal part x^{−}(t) i.e.

x(t) = x^{+}(t) + x^{−}(t)

For example, x(t) = e^{−at } can be written as

x(t) = e^{−at} u(t) + e^{−at }u(−t)

causal anti-causal

**Note:** Multiplying the signal by the unit step ensure that the resulting signal is causal.