GATE Electrical Engineering (EE) 2016 Shift 1 Solved Paper

Question : 44 of 65

Marks: +1, -0

Suppose

x_{1} (t)

and

x_{2} (t)

have the Fourier transforms as shown below.

Which one of the following statements is TRUE?

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

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