HW 04: Difference between revisions
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Find <math>\overbrace{10 [u(t-2) - u(t-3)]}^{x(t)} * \overbrace{e^{-t}u(t)}^{h(t)}</math> | Find <math>\overbrace{10 [u(t-2) - u(t-3)]}^{x(t)} * \overbrace{e^{-t}u(t)}^{h(t)}</math> | ||
[[Image: | [[Image:HW04.PNG]] | ||
<math>10 [u(t-2) - u(t-3)] * e^{-t}u(t) = </math> | <math>10 [u(t-2) - u(t-3)] * e^{-t}u(t) = | ||
\begin{cases} | |||
0, & t \le 2 \\ | |||
\int_{t-3}^{t-2} 10 \cdot e^{-\lambda} \,d\lambda, & t > 2\\ | |||
\end{cases} = \begin{cases} | |||
0, & t \le 2 \\ | |||
10\,e^{3-t}-10\,e^{2-t}, & t > 2\\ | |||
\end{cases} | |||
</math> |