# Causal System or not ?

#### Knigh7

Joined Feb 25, 2014
6
I cannot understand why this system isn't causal?
As a causal system only depends upon its current or previous inputs then this system should also be causal but the solutions say otherwise i don't get why...

y(t) = x(t/3)

Also I can understand that the system is stable but I was wondering if someone can show me mathematically as well?

Thanks...

#### WBahn

Joined Mar 31, 2012
30,048
What value of t does y(t) depend on if t = -9 sec?

#### Knigh7

Joined Feb 25, 2014
6
Oh...i see the point you made and it does make sense...but i had the idea since causal signals are zero for t < 0 so we are only supposed to check for t > 0 ?

And if thats not the case then how can we say that y(t) = x(t) is a causal signal because it can have any value x(t) for example for t = -3 ?
Do we have to assume that its zero for t < 0?

#### WBahn

Joined Mar 31, 2012
30,048
Signals are signals. they are neither causal nor non causal. It is systems that are causal or non causal.

A causal system means that it's response at time t is not dependent on the signal that arrive after time t. It does NOT mean that the signal does not exist after time t.

Similarly, a causal system's response at time t CAN depend on any part of a signal that occurred at or prior to time t. There is nothing magical about the moment in time that we hang the label t=0 to. What matters is the system response to signals at moments in time relative to the time of interest.