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Homework Help: Using an impulse response and an output to find an input using Z-transform

  1. May 1, 2012 #1
    1. The problem statement, all variables and given/known data
    An LTI digital system with impulse response h[n] = 2(1/4)^n u[n-1] produces an output y[n] = (-3)^n u[n-1]. Determine the corresponding input x[n].

    2. Relevant equations

    I believe that Y[z] = X[z]H[z]

    3. The attempt at a solution

    So I started by finding the z-transform of h[n]. Which I think is (0.25z)/(z-0.25)^2.

    I then went on the find to the z-transform of y[n]. Which I think is z/(z+3).

    So then I divided them and got 4((z-0.25)^2) / (z+3)..

    I can't figure out how to take the inverse z-transform to get x[n]. I think my z-transforms might be wrong, or I'm just dividing incorrectly.
  2. jcsd
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