Question

The message signal is used to SSB-SC modulate a sinusoidal carrier signal. If $f_{\infty }=2kHz,$ then the bandwidth of the resultant modulated signal will be ____kHz.

$m\left(t\right)={\left[\frac{sin\left(2\pi f_{m}t\right)}{\pi f_{m}t}\right]}^2$

• A. 4

Answer 1

The correct option is A 4
$m\left(t\right)={\left[\frac{sin\left(2\pi f_{m}t\right)}{\pi f_{m}t}\right]}^2=4sin{c}^2\left(2f_{m}t\right)$

$sinc\left(t\right)\stackrel{CIFT}{\leftarrow \to }rect\left(f\right)sinc\left(2f_{\pi t}t\right)\stackrel{CIFT}{\leftarrow \to }\frac{1}{2f_m}rect\left(\frac{f}{2f_m}\right)4sin{c}^2\left(2f_{m}t\right)\stackrel{CIFT}{\leftarrow \to }\frac{f}{f_m^2}[rect\left(\frac{f}{2f_m}\right)\ast rect\left(\frac{f}{2f_m}\right)]$


Bandwidth of $m\left(t\right)=2f_m=4kHz$

So, Bandwidth of SSB-SC signal =4 kHz