A causal signal is 0 for t<0

Question

I read the defination of causal system i.e. the system whose output only depends on the present and past value of signal and not on the future. I want to know-

• What is causal signal. Do causal system and signal implies same thing.
• explain how a causal signal x(t) = 0, for t<0 and a non causal signal x(t) = 0, for t>0. Like what is the actual concept or analogy behind this.

Answer 1

What is causal signal.

A causal signal is zero for negative time/indexes, i.e. $x(t) = 0 \forall t < 0$

Do causal system and signal implies same thing.

No. Apples and oranges. Signals and Systems are different things and it's important to understand the difference. This being said you can state

• The impulse response of a causal systems is a causal signal
• If a causal signal is inputted into a causal system, the output will also be a causal signal

explain how a causal signal x(t) = 0, for t<0 and a non causal signal x(t) = 0, for t>0.

That's incorrect. The definitions are

• Causal: $x(t) = 0 \forall t < 0$

• Anti-causal: $x(t) = 0 \forall t > 0$

• Non-causal: there are some non-zero values at both positive and negative times/indices