GATE EC 2015 Set 2 — Question 33
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Signals & Systems → Continuous-Time Signals → Aliasing & Reconstruction
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Question
The signal is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response . The filter output is
Correct answer
(A) (15)/(2) cos(40π t - (π)/(4) ight)
Solution
1.Input Signal: . Frequency Hz.
2.Sampling: Hz. The sampled signal spectrum contains impulses at Hz.
For , Hz. For , Hz.3.Filter: . The spectrum is a bandpass filter centered at Hz with bandwidth 1 Hz.
.4.Filtering: The filter selects the components at Hz from the sampled signal.
The component at Hz in is .Output at Hz: .
Output at Hz: .
5.Output Signal: . This matches option (A).
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