Question

The spectrum of a message signal m(t) is shown in the figure below.




If this message signal is applied to an FM modulator, whose frequency sensitivity is 10kH/V, then the bandwidth (using Carson's rule) of the resultant FM signal will be

Answer 1

(b)

$M\left(f\right)={10}^{-3}rect\left(\frac{f}{2000}\right)$

So, $f_{m(max)}=1000Hz=1kHz$

$m\left(t\right)=2sinc\left(2000t\right)V$

So, $|m\left(t\right){|}_{(max)}=2V$

Maximum frequency deviation
$\Delta f=k_f|m\left(t\right){|}_{max}=\left(10kHz/V\right)\times 2V=20kHz$

Deviation ratio, $D=\frac{\Delta f}{f_{m(max)}}=\frac{20}{1}=20$

Bandwidth$BW=(1+D)2f_{m(max)}$
= ( 1 + 20 )(2)(1)kHz
= 42 kHz