GATE EC 2014 Set 4 — Question 28
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Signals & Systems → Continuous-Time Signals → Frequency Response
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Question
A real-valued signal limited to the frequency band is passed through a linear time invariant system whose frequency response isThe output of the system is
Correct answer
(D) x(t - 2)
Solution
The output of an LTI system in the frequency domain is .
Given that is bandlimited to , for .
In the passband , .
Therefore, for all .
Using the time-shifting property of the Fourier Transform, .
Comparing with :
.
Thus, the output is , which corresponds to option (D).
Given that is bandlimited to , for .
In the passband , .
Therefore, for all .
Using the time-shifting property of the Fourier Transform, .
Comparing with :
.
Thus, the output is , which corresponds to option (D).
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