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| − | + | = Practice Question on Computing the Fourier Series discrete-time signal = | |
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| − | = Practice Question on Computing the Fourier Series discrete-time signal= | + | |
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| − | <math> | + | Obtain the Fourier series the DT signal |
| − | x[n] = \left\{ | + | |
| + | <math>x[n] = \left\{ | ||
\begin{array}{ll} | \begin{array}{ll} | ||
1, & \text{ for } -5\leq n \leq 5,\\ | 1, & \text{ for } -5\leq n \leq 5,\\ | ||
0, & \text{ for } 5< |n| \leq 10. | 0, & \text{ for } 5< |n| \leq 10. | ||
\end{array} | \end{array} | ||
| − | \right. \ </math> | + | \right. \ </math> |
| − | x[n] periodic with period 20. | + | x[n] periodic with period 20. |
---- | ---- | ||
| − | ==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 == |
| + | |||
| + | 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=== | + | |
| − | + | === Answer 1 === | |
| − | === | + | |
| − | Write it here. | + | Solution 1: ω<sub>o</sub> = <math>2*\pi/T = 2*pi/20=\pi/10</math> |
| − | ===Answer 3=== | + | a<sub>o</sub> is the DC value of the AC signal and is therefore 1/2 |
| − | Write it here. | + | |
| − | ---- | + | a<sub>k</sub> = <math> 1/20 * \int_a^b \! x(t)*e^{-j*k*(\pi/10)*t}\,dx </math> = <math>e^{j*k*\pi/2}-e^{-j*k*\pi/2}/(2*\pi*j*k) = sin(k*\pi/2)/(k*\pi)</math> |
| − | [[ | + | |
| + | <br> === Answer 2 === Write it here. === Answer 3 === Write it here. ---- [[2011 Spring ECE 301 Boutin|Back to ECE301 Spring 2011 Prof. Boutin]] | ||
| + | |||
| + | [[Category:ECE301Spring2011Boutin]] [[Category:Problem_solving]] | ||
Revision as of 12:47, 8 February 2011
Practice Question on Computing the Fourier Series discrete-time signal
Obtain the Fourier series the DT signal
$ x[n] = \left\{ \begin{array}{ll} 1, & \text{ for } -5\leq n \leq 5,\\ 0, & \text{ for } 5< |n| \leq 10. \end{array} \right. \ $
x[n] periodic with period 20.
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
Solution 1: ωo = $ 2*\pi/T = 2*pi/20=\pi/10 $ ao is the DC value of the AC signal and is therefore 1/2
ak = $ 1/20 * \int_a^b \! x(t)*e^{-j*k*(\pi/10)*t}\,dx $ = $ e^{j*k*\pi/2}-e^{-j*k*\pi/2}/(2*\pi*j*k) = sin(k*\pi/2)/(k*\pi) $
=== Answer 2 === Write it here. === Answer 3 === Write it here. ---- Back to ECE301 Spring 2011 Prof. Boutin
