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== CT signal == | == CT signal == | ||
| − | <math>x(t) = | + | <math>x(t) = cos({\frac{2\pi t}{3}})+ 4sin({\frac{5\pi t}{3}})\,</math> |
| − | + | ||
| − | + | ||
== Coefficients == | == Coefficients == | ||
Revision as of 17:32, 25 September 2008
CT signal
$ x(t) = 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_{-2} $,$ a_5 $,
$ a_{-5} $.
$ a_0 = 2, a_2 = a_-2 = \frac{1}{2}, a_5 = -2j, a_-5 = 2j $
