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Practice Question on Computing the Fourier Series coefficients of a discrete-time (sampled) cosine wave
Obtain the Fourier series coefficients of the DT signal
$ x[n] = \cos \left(3\pi n + \frac{\pi}{2} \right) . \ $
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Answer 1
for $ cos(n) $, the coefficients are $ a_1=\frac{1}{2},a_{-1}=\frac{1}{2}, a_k=0 \mbox{ for }k\ne 1,-1 $
Time shift property: $ x(n-n_0) \to e^{-jkw_0n_0}a_k $
Thus with $ w_0=3\pi\, $ and $ n_0=\frac{-\pi}{2} $,
$ a_1=\frac{e^{j 3 \pi \frac{\pi}{2}}}{2},a_{-1}=\frac{e^{-j 3 \pi \frac{\pi}{2}}}{2}, a_k=0 \mbox{ for }k\ne 1,-1 $
Is that right? I'm not sure about the time shift property.
--Cmcmican 21:53, 7 February 2011 (UTC)
Answer 2
Write it here.
Answer 3
Write it here.
