Topic: Electronics Engineering
Inverse Fourier transform of signal $X(j\omega)=2\pi\delta(\omega)+\pi\delta(\omega-4\pi)+\pi\delta(\omega+4\pi)$
- A. $1+cos~4\pi t$
- B. $\pi(1-cos~4\pi t)$
- C. $2\pi(1-cos~4\pi t)$
- D. $2\pi(1+cos~4\pi t)$
Answer: A. $1+cos~4\pi t$
Explanation: $X(j\omega)=2\pi\delta(\omega)+\pi\delta(\omega-4\pi)+\pi\delta(\omega+4\pi)$
$1 \leftarrow\frac{F.T.}\rightarrow 2\pi\delta(\omega)$
$cos~\omega_{0}t\leftarrow\frac{F.T.}\rightarrow\pi[\delta(\omega-\omega_{0})+\delta(\omega+\omega_{0})]$