(→Rewritten in e^{jw_0} Form) |
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==Rewritten in <math>e^{jw_0}</math> Form== | ==Rewritten in <math>e^{jw_0}</math> Form== | ||
| − | <math>x(t) = \frac{4\pi}{3} + \frac{1}{j2000}(e^{j1000\pi t}+e^{j-1000\pi t}) - \frac{1}{j1000}(e^{j1000\pi t}-e^{j-1000\pi t}) | + | <math>x(t) = \frac{4\pi}{3} + \frac{1}{j2000}(e^{j1000\pi t}+e^{j-1000\pi t}) - \frac{1}{j1000}(e^{j1000\pi t}-e^{j-1000\pi t})</math> |
==Fourier Series Coefficients== | ==Fourier Series Coefficients== | ||
Revision as of 10:11, 26 September 2008
Periodic CT Signal
$ x(t) = \frac{4\pi}{3} + \frac{1}{2}sin(1000\pi t) - cos(1000\pi t) \ $
Rewritten in $ e^{jw_0} $ Form
$ x(t) = \frac{4\pi}{3} + \frac{1}{j2000}(e^{j1000\pi t}+e^{j-1000\pi t}) - \frac{1}{j1000}(e^{j1000\pi t}-e^{j-1000\pi t}) $
Fourier Series Coefficients
$ a_0 = \frac{4\pi}{3} $
$ a_1 = \frac{1}{1000} $
$ w_0 = 1000\pi\ $
