- #1
dfx
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Homework Statement
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.
Homework Equations
[tex] \[ \int_{-\infty}^t f(t - \tau)g(\tau)\,d\tau\] [/tex]
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:
http://img58.imageshack.us/img58/8637/mspzk2.gif (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.
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