GATE EE 2017 Set 1 — Question 31
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Signals & Systems → Fourier Analysis & Sampling → Fourier Series (CT & DT)
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Question
Let the signalbe passed through an LTI system with frequency response , as given in the figure below
The Fourier series representation of the output is given as
Correct answer
(C) 4000 cos(2000π t)
Solution
The signal is a periodic impulse train with alternating signs. The period is s. The fundamental frequency is rad/s.
The Fourier series coefficients are .
Thus, for odd and for even.
The signal is
The LTI system is a low-pass filter with a cutoff frequency of and gain 1. Only the component at passes through.
Output .
The Fourier series coefficients are .
Thus, for odd and for even.
The signal is
The LTI system is a low-pass filter with a cutoff frequency of and gain 1. Only the component at passes through.
Output .
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