Causality problem

[adrianvon]

Hi all,

Can someone please guide me on how to determine if y(t) = e^-t cos(2ωt) is causal , where x(t) is cos(2ωt).

Am I correct if I say that first you have to select a negative value for t and then a positive value?

What value should I use for ω?

Any help would be highly appreciate.
Thanks.

 

[adrianvon]

i have another three questions:

1) Am I correct if I say that the output of the system below is dependent on two inputs?

y(t) = x(t-3) + x(3-t)

2) To check for causality, do I have to consider input x(t) only? For instance, in the system below, do I ignore cos(2t) ?

y(t) = cos(2t) x(3-t)

3) For y(t) = x^2(2-t) , since the input is not in the form of x(t) but x^2(t), is there another method of how to determine if the system is causal or not?

Thanks in advance for the help.

 

[adrianvon]

Any suggestions on these please?

 

[steveB]

Causal systems don't depend on future values. If you can find any violation of this it is not a causal system,

Take the example y(t)=x(3-t). If t=1. Then y(1)=x(2) which means that the present value of y depends on future values of x, and hence this is not a causal system.