Casual Function? (Electrical Engr)

[m453438]

Causal Function? (Electrical Engr)

Homework Statement

I have the following function:
d^2 y(t)/dt^2 + 3* dy(t)/dt + y(t) = dx(t)/dt +2x(t+1)

Where y(t) is the output and x(t) is the input.

I need to determine if it is causal or non causal.

Homework Equations

See above.

The Attempt at a Solution

My solution is that is causal since I can substitute t_1 = t+1 and t = t_1 -1, substituting this into the equation given:
d^2 y(t_1 -1)/dt^2 + 3* dy(t_1 -1)/dt + y(t_1 - 1) = dx(t_1 -1)/dt +2x(t_1)
And then if we say that t_1 = 0, I get:
d^2 y(-1)/dt^2 + 3* dy(-1)/dt + y(- 1) = dx(-1)/dt +2x(0)
And according to the definition, the equation does not depends on future inputs. Is my reasoning correct?
Thank You.

 

[cepheid]

No, your reasoning is not correct. Just by inspection of the equation, the system is
non-causal because the value of the output y at time t depends on the value of the input x at time t + 1 (one time step into the future).

Even with the change of variables you did (which didn't actually do anything): clearly if the output of the system at -1 sec depends on the input to the system 1 sec later at 0 sec, then causality is being violated.

 

[m453438]

Thank You cepheled.