GATE EE 2023 Set 1 — Question 63
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Signals & Systems → Fourier Analysis & Sampling → Aliasing & Reconstruction
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Question
A signal is sampled at 200 Hz and then passed through an ideal low pass filter having cut-off frequency of 100 Hz. The maximum frequency present in the filtered signal in Hz is _____________ (Round off to the nearest integer).
Correct answer
80 to 80
Solution
The signal can be expanded using the trigonometric identity :
.
The frequencies present in the original signal are Hz and Hz.
The sampling frequency is Hz. The Nyquist frequency is Hz.
Passing this through an ideal LPF with a cutoff of 100 Hz will allow both 60 Hz and 80 Hz to pass.
The maximum frequency present in the filtered signal is 80 Hz.
.
The frequencies present in the original signal are Hz and Hz.
The sampling frequency is Hz. The Nyquist frequency is Hz.
1.For Hz: Since , it is not aliased and remains at 60 Hz.
2.For Hz: Since , it will alias to Hz.
The sampled signal contains frequencies at 60 Hz and 80 Hz (among others). Passing this through an ideal LPF with a cutoff of 100 Hz will allow both 60 Hz and 80 Hz to pass.
The maximum frequency present in the filtered signal is 80 Hz.
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