GATE EC 2023 Set 1 Q35 — Analog Communications

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