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| − | + | = Practice Question on Computing the Fourier Series coefficients of a discrete-time (sampled) cosine wave = | |
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| − | = Practice Question on Computing the Fourier Series coefficients of a discrete-time (sampled) cosine wave= | + | |
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| − | <math>x[n] = \cos \left(3\pi n + \frac{\pi}{2} \right) . \ </math> | + | Obtain the Fourier series coefficients of the DT signal |
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| + | <math>x[n] = \cos \left(3\pi n + \frac{\pi}{2} \right) . \ </math> | ||
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| − | ==Share your answers below== | + | |
| − | 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! | + | == Share your answers below == |
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| + | 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! | ||
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| − | + | === Answer 1 === | |
| − | + | for <span class="texhtml">''c''''o''''s''(''n'')</span>, the coefficients are <math>a_1=\frac{1}{2},a_{-1}=\frac{1}{2}, a_k=0 \mbox{ for }k\ne 1,-1</math> | |
| − | + | Time shift property: <math>x(n-n_0) \to e^{-jkw_0n_0}a_k</math> | |
| − | <math> | + | Thus with <math>w_0=3\pi\,</math> and <math>n_0=\frac{-\pi}{2}</math>, |
| − | + | <math>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</math> | |
| − | --[[User:Cmcmican|Cmcmican]] 21:53, 7 February 2011 (UTC) | + | Is that right? I'm not sure about the time shift property. |
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| + | --[[User:Cmcmican|Cmcmican]] 21:53, 7 February 2011 (UTC) | ||
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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)) | ||
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| + | === Answer 2 === | ||
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| + | === Answer 3 === | ||
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| + | Write it here. | ||
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| − | [[ | + | |
| + | [[2011 Spring ECE 301 Boutin|Back to ECE301 Spring 2011 Prof. Boutin]] | ||
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| + | [[Category:ECE301Spring2011Boutin]] [[Category:Problem_solving]] | ||
Revision as of 15:36, 8 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))
Answer 2
Answer 3
Write it here.
