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GATE ECE 2002 | Question: 2.3

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The Laplace transform of a continuous-time signal $x(t)$ is $X(s)=\frac{5-s}{s^{2}-s-2}$. If the Fourier transform of this signal exists, then $x(t)$ is

  1. $e^{2 t} u(t)-2 e^{-t} u(t)$
  2. $-e^{2t} u(-t)+2 e^{-t} u(t)$
  3. $-e^{2 t} u(-t)-2 e^{-t} u(t)$
  4. $e^{2 t} u(-t)-2 e^{-t} u(t)$

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