dfx
Apr8-07, 03:55 PM
1. The problem statement, all variables and given/known data
Consider a linear system with the impulse response:
g(t) = 3x^2 - 4x + 7 for t>0 and 0 otherwise.
Find the output for the input f(t) = t for t \geq 0 and f(t) = 0 for t<0.
2. Relevant equations
\[ \int_{-\infty}^t f(t - \tau)g(\tau)\,d\tau\]
3. The attempt at a solution
\[ \int_0^t f(t - \tau)g(\tau)\,d\tau\]
\[ \int_0^t (t - \tau)(3\tau^2 - 4\tau + 7\,d\tau\)]
and the answer I keep getting is
\frac{t^4}{4} - \frac{2t^3}{3} + \frac{7t^2}{2}
whereas the official given answer has the sign in the middle term as a plus: +\frac{2t^3}{3}
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.
Consider a linear system with the impulse response:
g(t) = 3x^2 - 4x + 7 for t>0 and 0 otherwise.
Find the output for the input f(t) = t for t \geq 0 and f(t) = 0 for t<0.
2. Relevant equations
\[ \int_{-\infty}^t f(t - \tau)g(\tau)\,d\tau\]
3. The attempt at a solution
\[ \int_0^t f(t - \tau)g(\tau)\,d\tau\]
\[ \int_0^t (t - \tau)(3\tau^2 - 4\tau + 7\,d\tau\)]
and the answer I keep getting is
\frac{t^4}{4} - \frac{2t^3}{3} + \frac{7t^2}{2}
whereas the official given answer has the sign in the middle term as a plus: +\frac{2t^3}{3}
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.