Suppose $x_{1}(t)$ and $x_{2}(t)$ have the Fourier transforms as shown below.

Which one of the following statements is TRUE?

1. $x_{1}(t)$ and $x_{2}(t)$ are complex and $x_{1}(t) x_{2}(t)$is also complex with nonzero imaginary part
2. $x_{1}(t)$ and $x_{2}(t)$ are real and $x_{1}(t) x_{2}(t)$is also real
3. $x_{1}(t)$ and $x_{2}(t)$ are complex but $x_{1}(t) x_{2}(t)$ is real
4. $x_{1}(t)$ and $x_{2}(t)$ are imaginary but $x_{1}(t) x_{2}(t)$ is real

recategorized