(New page: Category:ECE301Spring2011Boutin Category:problem solving = Practice Question on Computing the Fourier Series coefficients of a sine wave= Obtain the Fourier series coefficients of ...) |
|||
| Line 11: | Line 11: | ||
---- | ---- | ||
===Answer 1=== | ===Answer 1=== | ||
| − | + | ||
| + | for <math>sin(t)</math>, the coefficients are <math>a_1=\frac{1}{2j},a_{-1}=\frac{-1}{2j}, a_k=0 \mbox{ for }k\ne 1,-1</math> | ||
| + | |||
| + | Time shift property: <math>x(t-t_0) \to e^{-jkw_0t_0}a_k</math> | ||
| + | |||
| + | Thus with <math>w_0=3\pi\,</math> and <math>t_0=\frac{-\pi}{2}</math>, | ||
| + | |||
| + | <math>a_1=\frac{e^{j 3 \pi \frac{\pi}{2}}}{2j},a_{-1}=\frac{-e^{-j 3 \pi \frac{\pi}{2}}}{2j}, a_k=0 \mbox{ for }k\ne 1,-1</math> | ||
| + | |||
| + | Is that right? I'm not sure about the time shift property. | ||
| + | |||
| + | --[[User:Cmcmican|Cmcmican]] 21:09, 7 February 2011 (UTC) | ||
| + | |||
| + | |||
===Answer 2=== | ===Answer 2=== | ||
Write it here. | Write it here. | ||
Revision as of 17:09, 7 February 2011
Contents
Practice Question on Computing the Fourier Series coefficients of a sine wave
Obtain the Fourier series coefficients of the CT signal
$ x(t) = \sin \left(3\pi t + \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 $ sin(t) $, the coefficients are $ a_1=\frac{1}{2j},a_{-1}=\frac{-1}{2j}, a_k=0 \mbox{ for }k\ne 1,-1 $
Time shift property: $ x(t-t_0) \to e^{-jkw_0t_0}a_k $
Thus with $ w_0=3\pi\, $ and $ t_0=\frac{-\pi}{2} $,
$ a_1=\frac{e^{j 3 \pi \frac{\pi}{2}}}{2j},a_{-1}=\frac{-e^{-j 3 \pi \frac{\pi}{2}}}{2j}, a_k=0 \mbox{ for }k\ne 1,-1 $
Is that right? I'm not sure about the time shift property.
--Cmcmican 21:09, 7 February 2011 (UTC)
Answer 2
Write it here.
Answer 3
Write it here.
