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<math>x(t) = cos(3\pi t+\pi) \!</math> with fundamental frequency of <math>\pi</math> | <math>x(t) = cos(3\pi t+\pi) \!</math> with fundamental frequency of <math>\pi</math> | ||
| + | <math>x(t) = \frac{e^{j(3\pi t+\pi)}+e^{-j(3\pi t+\pi)}</math> | ||
| − | + | ||
| − | <math>x(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 16:35, 26 September 2008
Periodic CT Signal
$ x(t) = cos(3\pi t+\pi) \! $ with fundamental frequency of $ \pi $ $ x(t) = \frac{e^{j(3\pi t+\pi)}+e^{-j(3\pi t+\pi)} $
$ 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\ $
