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[[Category:ECE301Spring2011Boutin]]
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= Practice Question on Computing the Fourier Series coefficients of a discrete-time (sampled) cosine wave =
[[Category:problem solving]]
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= Practice Question on Computing the Fourier Series coefficients of a discrete-time (sampled) cosine wave=
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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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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==
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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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== 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 <math>cos(n)</math>,  the coefficients are <math>a_1=\frac{1}{2},a_{-1}=\frac{1}{2}, a_k=0 \mbox{ for }k\ne 1,-1</math>
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=== Answer 1 ===
  
Time shift property:  <math>x(n-n_0) \to e^{-jkw_0n_0}a_k</math>
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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>  
  
Thus with <math>w_0=3\pi\,</math> and <math>n_0=\frac{-\pi}{2}</math>,
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Time shift property: <math>x(n-n_0) \to e^{-jkw_0n_0}a_k</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>
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Thus with <math>w_0=3\pi\,</math> and <math>n_0=\frac{-\pi}{2}</math>,
  
Is that right?  I'm not sure about the time shift property.
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<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)
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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.
  
===Answer 2===
 
Write it here.
 
===Answer 3===
 
Write it here.
 
 
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[[2011_Spring_ECE_301_Boutin|Back to ECE301 Spring 2011 Prof. Boutin]]
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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 16:36, 8 February 2011

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) . \ $


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!


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.


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