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Student Question: Since this is DT and not CT, shouldn't the focus be on N=2 and not <span class="texhtml">''w''<sub>''o''</sub></span>? ([[User:Clarkjv|Clarkjv]] 20:36, 8 February 2011 (UTC)) | Student Question: Since this is DT and not CT, shouldn't the focus be on N=2 and not <span class="texhtml">''w''<sub>''o''</sub></span>? ([[User:Clarkjv|Clarkjv]] 20:36, 8 February 2011 (UTC)) | ||
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| + | Student Response: Yeah, it should be. I did this before today's lecture, and made some mistakes. I'm posting a new answer in answer 2. --[[User:Cmcmican|Cmcmican]] 19:46, 9 February 2011 (UTC) | ||
=== Answer 2 === | === Answer 2 === | ||
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=== Answer 3 === | === Answer 3 === | ||
Revision as of 14:46, 9 February 2011
Contents
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) . \ $
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
for c'o's(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)
Student Question: Since this is DT and not CT, shouldn't the focus be on N=2 and not wo? (Clarkjv 20:36, 8 February 2011 (UTC))
Student Response: Yeah, it should be. I did this before today's lecture, and made some mistakes. I'm posting a new answer in answer 2. --Cmcmican 19:46, 9 February 2011 (UTC)
Answer 2
Answer 3
Write it here.
