GATE EC 2021 Set 1 — Question 14
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Signals & Systems → Continuous-Time Signals → Sampling Theorem
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Question
Consider a real-valued base-band signal , band limited to . The Nyquist rate for the signal is ________
Correct answer
(B) 30 kHz
Solution
The signal is bandlimited to . The signal is a time-scaled and shifted version. Time scaling by (expansion in time) results in compression in frequency. Specifically, . If is non-zero for , then is non-zero for . Thus, the bandwidth of is .The product in time corresponds to convolution in frequency: . The bandwidth of the convolution of two signals is the sum of their individual bandwidths. Therefore, the bandwidth of is .The Nyquist rate is twice the maximum frequency component: .
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