Problem 예제.

Multiple Choice • Views 815 • Comments 0 • Last Updated at 4 months ago

두 함수 $f_1(t) = 1, \quad f_2(t)=e^{-t}$ 일 때 합성 적분(convolution)값은?

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$1-e^{-t}$

$\dfrac{1}{1-e^{-t}}$

$\dfrac{1}{1+e^{-t}}$

$1+e^{-t}$

Solution

$\mathcal{L} (f_1(t) * f_2(t) ) = F_1(s) \cdot F_2(s) = \dfrac{1}{s} \cdot \dfrac{1}{s+1}$

$\mathcal{L}^{-1} \left( \dfrac{1}{s} \cdot \dfrac{1}{s+1} \right) = \mathcal{L}^{-1} \left( \dfrac{1}{s} - \dfrac{1}{s+1} \right) = 1 - e^{-t}$

Correct answer: 1