Topic: Electronics Engineering
The Fourier transform of a signal $x(t)=e^{-4|t|}$ is
- A. $8/(16+\omega^{2})$
- B. $-8/(16-\omega^{2})$
- C. $4/(16+\omega^{2})$
- D. $-4/(16+\omega^{2})$
Answer: A. $8/(16+\omega^{2})$
Explanation: $x(t) = e^{-4|t|} = e^{-4t}u(t) + e^{4t}u(-t)$. The Fourier transform of $e^{-a|t|}$ is $\frac{2a}{a^{2}+\omega^{2}}$. Substituting $a=4$, $X(\omega) = \frac{2(4)}{4^{2}+\omega^{2}} = \frac{8}{16+\omega^{2}}$.