Question

A device with input $x\left(t\right)$ and output $y\left(t\right)$ is characterized by $y\left(t\right)=x^2\left(t\right)$. An FM signal with frequency deviation of $90kHz$ and modulating signal bandwidth of $5kHz$ is applied to this device. The bandwidth of the output signal is

• A. $370kHz$
• B. $190kHz$
• C. $380kHz$
• D. $95kHz$

Answer 1

The correct option is C $380kHz$

For $x\left(t\right)$, $BW=2(\Delta \omega +\omega )$
$\Delta \omega$ is deviation and $\omega$ is the band width of modulating signal.
$\therefore BW=2(90+5)=190$
For $x^2\left(t\right)$, $BW=2\times 190=380$