GATE EC 2014 Set 3 — Question 27
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Signals & Systems → Continuous-Time Signals → Aliasing & Reconstruction
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Question
Let be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are
Correct answer
(A) 5 Hz and 15 Hz only
Solution
The signal is . The frequencies present are Hz and Hz.
The sampling frequency is Hz.
The sampled signal contains frequencies of the form .
For Hz:
For Hz:
The reconstruction filter is an ideal low-pass filter with a cut-off frequency of 20 Hz. Therefore, it will pass all frequency components below 20 Hz.
From the sampled components, 5 Hz and 15 Hz are both less than 20 Hz.
Thus, the reconstructed signal will contain 5 Hz and 15 Hz components.
The sampling frequency is Hz.
The sampled signal contains frequencies of the form .
For Hz:
For Hz:
The reconstruction filter is an ideal low-pass filter with a cut-off frequency of 20 Hz. Therefore, it will pass all frequency components below 20 Hz.
From the sampled components, 5 Hz and 15 Hz are both less than 20 Hz.
Thus, the reconstructed signal will contain 5 Hz and 15 Hz components.
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