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<math> = -\frac{1}{2}e^{j3\pi t}-\frac{1}{2}e^{-j3\pi t}</math> | <math> = -\frac{1}{2}e^{j3\pi t}-\frac{1}{2}e^{-j3\pi t}</math> | ||
| − | |||
==Fourier Series Coefficients== | ==Fourier Series Coefficients== | ||
| − | <math> | + | <math>a_3 = -\frac{1}{2}</math> |
| − | <math> | + | <math>a_-3 = -\frac{1}{2}</math> |
| − | + | ||
| − | + | ||
Revision as of 17:43, 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)}}{2} $
$ = \frac{e^{j3\pi t}e^{\pi}+e^{-j3\pi t}e^{\pi}}{2} $
$ = \frac{-e^{j3\pi t}-e^{-j3\pi t}}{2} $
$ = -\frac{1}{2}e^{j3\pi t}-\frac{1}{2}e^{-j3\pi t} $
Fourier Series Coefficients
$ a_3 = -\frac{1}{2} $
$ a_-3 = -\frac{1}{2} $
