GATE EC 2026 Set 1 — Question 57
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Communications → Analog Communications → AM Modulation & Demodulation
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Question
Consider a real, narrowband signal where the maximum frequency components of and are and , respectively.Which of the following statements is/are correct for ?
Correct answer
(A) x(t) represents a PSK modulated signal for suitable choices of A(t) and θ(t).; (B) x(t) represents an amplitude modulated signal for suitable choices of A(t) and θ(t).; (C) x(t) represents a band-limited Gaussian noise process.
Solution
The given expression is the general canonical representation for any narrowband signal.
1.PSK (Phase Shift Keying): If we choose (a constant) and to take discrete values (e.g., or for BPSK), the signal represents a PSK modulated signal. Thus, statement (A) is correct.
2.AM (Amplitude Modulation): If we choose (or a constant) and , the signal represents a standard AM signal. Thus, statement (B) is correct.
3.Gaussian Noise Process: A narrowband Gaussian noise process can be represented in polar form as , where is the Rayleigh-distributed envelope and is the uniformly distributed phase. Since this matches the given form, statement (C) is correct as a representation of such a process.
4.Narrowband FM: A narrowband FM signal is defined as , which can be converted into the envelope-phase form . Therefore, can represent a narrowband FM signal, making the "never" in statement (D) incorrect.
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