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GATE 2026 EC – Question 57

Communications · Analog Communications · 2 marks · Multiple select

Consider a real, narrowband signal $x(t)=A(t)\cos[2\pi f_ct+\theta(t)]$ where the maximum frequency components of $A(t)$ and $\theta(t)$ are $f_M$ and $f_c\,(=1000f_M)$, respectively. Which of the following statements is/are correct for $-\infty<t<\infty$?

  1. $x(t)$ represents a PSK modulated signal for suitable choices of $A(t)$ and $\theta(t)$.
  2. $x(t)$ represents an amplitude modulated signal for suitable choices of $A(t)$ and $\theta(t)$.
  3. $x(t)$ represents a band-limited Gaussian noise process.
  4. $x(t)$ never represents a narrowband FM signal.

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Show answer and explanation

Correct answer: (A) $x(t)$ represents a PSK modulated signal for suitable choices of $A(t)$ and $\theta(t)$.; (B) $x(t)$ represents an amplitude modulated signal for suitable choices of $A(t)$ and $\theta(t)$.

Explanation

The general envelope-phase form covers PSK (constant A, binary θ), AM (θ constant) and narrowband FM, so D is false. C is not correct, since the given deterministic form does not by itself represent a Gaussian noise process.