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Homework Help: Casual Function? (Electrical Engr)

  1. Jun 15, 2010 #1
    Causal Function? (Electrical Engr)

    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    See above.


    3. 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.
     
    Last edited: Jun 15, 2010
  2. jcsd
  3. Jun 15, 2010 #2

    cepheid

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    Staff Emeritus
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    Gold Member

    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.
     
  4. Jun 18, 2010 #3
    Thank You cepheled.
     
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