GATE EC 2018 Set 1 — Question 64
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Signals & Systems → Continuous-Time Signals → Aliasing & Reconstruction
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Question
A band limited low-pass signal of bandwidth 5 kHz is sampled at a sampling rate . The signal is reconstructed using the reconstruction filter whose magnitude response is shown below:
The minimum sampling rate (in kHz) for perfect reconstruction of is _______.
Correct answer
13 to 13
Solution
The bandwidth of the low-pass signal is kHz. The spectrum of the sampled signal contains replicas of the original spectrum centered at integer multiples of the sampling frequency .The baseband replica occupies the frequency range kHz. The first replica is centered at and occupies the range kHz.For perfect reconstruction, the reconstruction filter must:
1.Pass the baseband signal without distortion. The filter's passband extends to 6 kHz, which is greater than the signal bandwidth of 5 kHz. Thus, the signal is passed correctly.
2.Completely reject all other replicas. The filter's stopband starts at 8 kHz. Therefore, the lower edge of the first replica must be at or above 8 kHz to be fully rejected.
The minimum sampling rate required is 13 kHz.Continue learning with Success Tracker
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