Discussion :: Exam Questions Paper
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Consider the signal x(n) = 1 + sin
n + 3 cosn + cos 
. Then Fourier series coefficients are __________ .
|
A.
1,
 -  j, + j, j, - j |
|
B.
1,
+ j, - j, - j , + j |
|
C.
1, 3 -
j, 3 + j, j, - j |
|
D.
1, 3 + j, 3 - j, - j, + j
|
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Answer : Option A
Explanation :
The signal x(n) = 1 + sinn 3 cos n + cos n + cos
is periodic with period N, and we can expand x[n] directly in terms of complex exponentials to obtain
Collecting terms, we find that
Thus for Fourier series coefficients for this example are
a0 = 1,
a1 = +
= -j,
a-1 = - = +j,
a2 = j,
a-2 = -j.
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