GATE EC 2023 Set 1 — Question 50
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Signals & Systems → Continuous-Time Signals → Sampling Theorem
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Question
Let and be two band-limited signals having bandwidth rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample , is
Correct answer
(D) 32π × 10³
Solution
The bandwidth of and is rad/s.
For the first branch: . The maximum frequency is rad/s.
For the second branch: . The maximum frequency is rad/s.
The output is the sum of these two signals, so its maximum frequency is rad/s.
The Nyquist sampling frequency is rad/s.
For the first branch: . The maximum frequency is rad/s.
For the second branch: . The maximum frequency is rad/s.
The output is the sum of these two signals, so its maximum frequency is rad/s.
The Nyquist sampling frequency is rad/s.
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