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Let a frequency modulated $\text{(FM)}$ signal

$x(t)=A \cos \left(\omega_{c} t+k_{f} \int_{-\infty}^{t} m(\lambda) d \lambda\right)$, where $m(t)$ is a message signal of bandwidth $\text{W.}$ It is passed through a non-linear system with output $y(t)=2 x(t)+5(x(t))^{2}$. Let $B_{T}$ denote the $\text{FM}$ bandwidth. The minimum value of $\omega_{c}$ required to recover $x(t)$ from $y(t)$ is 
 

  1. $B_{T}+W$
  2. $\frac{3}{2} B_{T}$
  3. $2 B_{T}+W$
  4. $\frac{5}{2} B_{T}$

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