Question

$\text{The amplitude of a sinusoidal carrier signal is modulated by tthe message signal, m(t)=}\text{sinc(1000t)sinc}{}^2\text{(2000t). The bandwidth of the resultant AM signal will be\_\_\_\_\_\_\_\_\_\_kHz}\text{Assume that, sinc(t)=sin}\left(\pi t/\pi t\right)$

• A. 5

Answer 1

The correct option is A 5
$\text{sinc(t)}\stackrel{CTFT}{⟷}rect\left(f\right)\text{sinc(1000t)}\stackrel{CTFT}{⟷}{10}^{-3}rect\left(\frac{f}{1000}\right)\text{sinc(2000t)}\stackrel{CTFT}{⟷}\frac{{10}^{-3}}{2}rect\left(\frac{f}{2000}\right){\text{Sinc}}^2\left(2000t\right)\stackrel{CTFT}{⟷}\frac{{10}^{-3}}{2}rect\left(\frac{f}{2000}\right)\ast \frac{{10}^{-3}}{2}rect\left(\frac{f}{2000}\right)M\left(f\right)={10}^{-3}rect\left(\frac{f}{2000}\right)\ast \frac{{10}^{-3}}{2}rect\left(\frac{f}{2000}\right)\ast \frac{{10}^{-3}}{2}rect\left(\frac{f}{2000}\right)\text{So,}{f}_{m}max=2.5kHz(BW{)}_{AM}=2f_{m\left(max\right)}=5kHz$