GATE EC 2017 Set 1 — Question 52
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Signals & Systems → LTI Systems → Filters & Bandwidth
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Question
A continuous time signal , where is in seconds, is the input to a linear time invariant (LTI) filter with the impulse responseLet be the output of this filter. The maximum value of is ______.
Correct answer
7.9 to 8.1
Solution
The impulse response of the filter is given by .
Taking the Fourier transform to find the frequency response :
Using the property , we can rewrite as:
This is an ideal low-pass filter with a gain of 2 and a cutoff frequency Hz.The input signal is .
The frequencies present in the input are:
Hz
HzEvaluating the filter response at these frequencies:
For Hz: , so .
For Hz: , so .The output signal is:
The maximum value of is 8.
Taking the Fourier transform to find the frequency response :
Using the property , we can rewrite as:
This is an ideal low-pass filter with a gain of 2 and a cutoff frequency Hz.The input signal is .
The frequencies present in the input are:
Hz
HzEvaluating the filter response at these frequencies:
For Hz: , so .
For Hz: , so .The output signal is:
The maximum value of is 8.
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