GATE EE 2014 Set 3 — Question 44
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Signals & Systems → Fourier Analysis & Sampling → Aliasing & Reconstruction
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Question
A sinusoid of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with a cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that has a frequency of
Correct answer
(C) 30 Hz
Solution
Sampling frequency Hz. The sampled signal contains frequency components at . The ideal lowpass filter has a cutoff frequency of 25 Hz. The output is a sinusoid of frequency 20 Hz. This implies that one of the aliased components falls at 20 Hz and is within the filter's passband ().Thus, Hz for some integer .
For : Hz or Hz.
Checking the options, 30 Hz is given in option (C).
For : Hz or Hz.
Checking the options, 30 Hz is given in option (C).
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