Difference between revisions of "Problem 5 - Solving non-graphically (alternate solution) Old Kiwi" - Rhea

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-To convolve two functions we have the following:
- <math>
-y(t) = h(t) * x(t) = \int_{-\infty}^\infty x(t)h(t-\tau)d\tau
-</math>
-Plugging in functions for x(t) and h(t) we get:
- <math>
-= \int_{-\infty}^\infty e^{-\tau}u(\tau)u(t-1-\tau)d\tau
-</math>
-We now change the interval of integration to reflect the step function <math>u(\tau)</math>
- <math>
-= \int_{0}^\infty e^{-\tau}u(t-1-\tau)d\tau
-</math>
-Finally, by changing the interval of integration once again we get:
- <math>
-\begin{align}
-&= \int_{0}^{t-1} e^{-\tau}d\tau \\
-&= -e^{-(t-1)} - (-e^{0}) \\
-&= 1 - e^{-(t-1)}
-\end{align}
-</math>

Latest revision as of 22:12, 1 July 2008