GATE EC 2023 Set 1 — Question 49
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Signals & Systems → Continuous-Time Signals → Fourier Transform & Properties
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Question
Let be passed through an LTI system having impulse response . The output of the system is
Correct answer
(A) ((15W)/(4)) cos(10.5Wt)
Solution
The impulse response is where .
Taking the Fourier transform of :
where is the triangular function with base width and height 1.
The frequency response is:
The input signal has a frequency .
Evaluating at :
The output is:
Taking the Fourier transform of :
where is the triangular function with base width and height 1.
The frequency response is:
The input signal has a frequency .
Evaluating at :
The output is:
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