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
- $B_{T}+W$
- $\frac{3}{2} B_{T}$
- $2 B_{T}+W$
- $\frac{5}{2} B_{T}$