GATE EC 2016 Set 3 — Question 40
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Signals & Systems → Continuous-Time Signals → Fourier Series
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Question
A signal is the input to an LTI system with the transfer functionIf denotes the coefficient in the exponential Fourier series of the output signal, then is equal to
Correct answer
(B) 1
Solution
The input signal is .
The frequencies are and .
The fundamental frequency .
Expressing in terms of :
Using Euler's formula:
The input Fourier coefficients are .
The transfer function is . The frequency response is .
The output Fourier coefficients are .
We need .
The frequencies are and .
The fundamental frequency .
Expressing in terms of :
Using Euler's formula:
The input Fourier coefficients are .
The transfer function is . The frequency response is .
The output Fourier coefficients are .
We need .
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