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Quick convolution integral checking

  1. Apr 8, 2007 #1

    dfx

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

    Consider a linear system with the impulse response:

    g(t) = [tex] 3x^2 - 4x + 7 [/tex] for t>0 and 0 otherwise.

    Find the output for the input f(t) = t for [tex] t \geq 0 [/tex] and f(t) = 0 for t<0.

    2. Relevant equations

    [tex] \[ \int_{-\infty}^t f(t - \tau)g(\tau)\,d\tau\] [/tex]


    3. The attempt at a solution

    [tex] \[ \int_0^t f(t - \tau)g(\tau)\,d\tau\] [/tex]

    [tex] \[ \int_0^t (t - \tau)(3\tau^2 - 4\tau + 7\,d\tau\)] [/tex]

    and the answer I keep getting is

    [tex] \frac{t^4}{4} - \frac{2t^3}{3} + \frac{7t^2}{2} [/tex]

    whereas the official given answer has the sign in the middle term as a plus: [tex] +\frac{2t^3}{3} [/tex]

    I've even tried wolfram and I think I'm correct:

    [​IMG] (obviously with different variables - x instead of tau, but still evaluted between t and 0).

    If anyone could clear up the correct answer that would be much appreciated.
     
    Last edited: Apr 8, 2007
  2. jcsd
  3. Apr 9, 2007 #2

    dfx

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    ...anyone?
     
  4. Apr 9, 2007 #3
    Even I got the same answer as you. So I guess not much of a help.
     
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