# Find the Laplace transform of the signal x(t)=te^-2|t|.

+1 vote
Find the Laplace transform of the signal x(t)=te^-2|t|.

(a) $-\frac{1}{(s-2)^2} + \frac{1}{(s+2)^2}$

(b) $\frac{1}{(s-2)^2} + \frac{1}{(s+2)^2}$

(c) $\frac{1}{(s-2)^2} – \frac{1}{(s+2)^2}$

(d) $-\frac{1}{(s-2)^2} – \frac{1}{(s+2)^2}$

I have been asked this question during an interview.

The question is from The Laplace Transform topic in portion Laplace Transform and System Design of Signals and Systems

by (42.1k points)
Right choice is (a) $-\frac{1}{(s-2)^2} + \frac{1}{(s+2)^2}$

The explanation is: Given  x(t)=te^-2|t|

L{x(t)} = X(s) = $\int_{-∞}^∞ x(t) e^{-st} \,dt = \int_{-∞}^∞ te^{-2|t|} e^{st} \,dt$

=$\int_{-∞}^0 te^{2t} e^{-st} \,dt + \int_0^∞ te^{-2t} e^{-st} \,dt = -\frac{1}{(s-2)^2} + \frac{1}{(s+2)^2}$.

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