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Homework Help: Causal system/convolution question

  1. Oct 20, 2014 #1
    1. The problem statement, all variables and given/known data

    a) find if the system is causal.
    b) find the impulse response

    given: y(t)=x(t-1)u(t)

    a) Causal
    b) delta(t-1)

    2. Relevant equations

    3. The attempt at a solution


    I thought this is a non-causal system because if our input is delta(t), the resultant output is delta(t-1)
    if t=1, input value depends on delta(1), and its output is delta(0). output depends on future value.

    b) I don't know where that u(t) comes from...

  2. jcsd
  3. Oct 21, 2014 #2


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    Homework Helper

    Usually this type of problem will the additional condition that x(t) = 0 for t<0, so that it is more clear that this is a weighted ( by u(t) ) shift operation.
    I am assuming that x and u are known and y is the output.
  4. Oct 21, 2014 #3


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    Gold Member

    a) The system is causal because the output is only dependent on past values of input x[t-1] is a time in the past.

    b) y[t]=x[t-1]*u[t] --> for the impulse response, we put delta function as input (x) and then solve for output. so, impulse response:
    h[t] = delta[t-1]*u[t] = delta[t-1]
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