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Then we can know the fundamental frequency is <math>\frac{\pi}{3}</math>. <br> | Then we can know the fundamental frequency is <math>\frac{\pi}{3}</math>. <br> | ||
| − | Also, we can get coefficients a_0, a_2, a_5, a_-2, a_-5. | + | Also, we can get coefficients <math>a_0, a_2, a_5, a_-2, a_-5</math>. |
| + | <math>a_0 = 2, a_2 = a_-2 = \frac{1}{2}, a_5 = -2j, a_-5 = 2j</math> | ||
Revision as of 16:23, 21 September 2008
CT signal
$ x(t) = 2 + cos({\frac{2\pi t}{3}})+ 4sin({\frac{5\pi t}{3}})\, $
Coefficients
$ cos({\frac{2\pi t}{3}}) = \frac{1}{2}e^{\frac{j2\pi t}{3}} + \frac{1}{2}e^{\frac{-j2\pi t}{3}} $
$ 4sin({\frac{5\pi t}{3}}) = -2je^{\frac{j5\pi t}{3}} + 2je^{\frac{-j5\pi t}{3}} $
$ x(t) = 2 + \frac{1}{2}e^{\frac{j2\pi t}{3}} + \frac{1}{2}e^{\frac{-j2\pi t}{3}} -2je^{\frac{j5\pi t}{3}} + 2je^{\frac{-j5\pi t}{3}} $
$ x(t) = 2 + \frac{1}{2}e^{\frac{2j2\pi t}{6}} + \frac{1}{2}e^{\frac{-2j2\pi t}{6}} -2je^{\frac{2j5\pi t}{6}} + 2je^{\frac{-2j5\pi t}{6}} $
Then we can know the fundamental frequency is $ \frac{\pi}{3} $.
Also, we can get coefficients $ a_0, a_2, a_5, a_-2, a_-5 $.
$ a_0 = 2, a_2 = a_-2 = \frac{1}{2}, a_5 = -2j, a_-5 = 2j $
