GATE EC 2026 Set 1 Q47 — Analog Communications

Consider a real, narrowband signal $x(t)=A(t) \cos \left[2 \pi f_{c} t+\theta(t)\right]$ where the maximum frequency components of $A(t)$ and $\theta(t)$ are $f_{M}$ and $f_{c}\left(=1000 f_{M}\right)$, respectively.

Which of the following statements is/are correct for $-\infty < t < \infty ?$