GATE EE 2017 Set 2 — Question 31
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Signals & Systems → Fourier Analysis & Sampling → Sampling Theorem
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Question
The output of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is
Correct answer
(B) 1500 samples/s
Solution
1.Analyze the input spectrum: The input signal has a Fourier transform which is a triangle band-limited to rad/s.
2.Effect of multiplication: The signal is multiplied by , resulting in . In the frequency domain, this corresponds to shifting the spectrum:
Since spans , the shifted components span:3.Effect of the filter: The signal passes through a filter with impulse response . This is an ideal low-pass filter with a frequency response that is for and otherwise.
4.Output spectrum: The output has a spectrum . The filter truncates the spectrum of at rad/s. Therefore, is band-limited to rad/s.
5.Calculate sampling rate: The maximum frequency in Hz is:
According to the Nyquist sampling theorem, the minimum sampling rate required for unique reconstruction is:Thus, the correct option is (B).Continue learning with Success Tracker
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