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Q1:

Consider the signal x(n) = 1 + sinn + 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

ANS:A -

1, - j, + j, j, - j

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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