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<math>a_k=\frac{1}{T} \int_0^Tx(t)e^{-jk\omega_ot}dt</math> | <math>a_k=\frac{1}{T} \int_0^Tx(t)e^{-jk\omega_ot}dt</math> | ||
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| + | Going to conver the equation into signal that is all in exponentials. | ||
| + | |||
| + | <math>\frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + \frac{1}{2}(e^{j3\pi t} + e^{-j3\pi t}) + e^{j2\pi t}</math> | ||
Revision as of 19:18, 25 September 2008
The Signal
mmm lets randomly take...
$ \sin4\pi t + \cos3\pi t + e^{j2\pi t} $
The Coefficients
Remeber... $ x(t) = \sum^{\infty}_{k = -\infty} a_k e^{jk\pi t}\, $
$ a_k=\frac{1}{T} \int_0^Tx(t)e^{-jk\omega_ot}dt $
Going to conver the equation into signal that is all in exponentials.
$ \frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + \frac{1}{2}(e^{j3\pi t} + e^{-j3\pi t}) + e^{j2\pi t} $
