(New page: ==Periodic CT Signal== <math>x(t) = 2sin(1000\pi t) + \frac{4\pi}{3} - cos(2000\pi t)\ </math> ==Fourier Series Coefficients==) |
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==Periodic CT Signal== | ==Periodic CT Signal== | ||
| − | <math>x(t) = | + | <math>x(t) = \frac{4\pi}{3} + \frac{1}{2}sin(1000\pi t) - cos(1000\pi t) \ </math> |
| + | |||
| + | ==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> | ||
==Fourier Series Coefficients== | ==Fourier Series Coefficients== | ||
| + | <math>a_0 = \frac{4\pi}{3}</math> | ||
| + | |||
| + | <math>a_1 = \frac{1}{1000}</math> | ||
| + | |||
| + | <math>w_0 = 1000\pi\ </math> | ||
Revision as of 09:10, 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\ $
