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| + | [[Category:problem solving]] | ||
| + | [[Category:ECE301]] | ||
| + | [[Category:ECE]] | ||
| + | [[Category:Fourier series]] | ||
| + | [[Category:signals and systems]] | ||
| + | |||
| + | == Example of Computation of Fourier series of a CT SIGNAL == | ||
| + | A [[Signals_and_systems_practice_problems_list|practice problem on "Signals and Systems"]] | ||
| + | ---- | ||
| + | |||
==Periodic CT Signal== | ==Periodic CT Signal== | ||
<math>x(t) = \frac{4\pi}{3} + \frac{1}{2}sin(1000\pi t) - cos(1000\pi t) \ </math> | <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== | ==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== | ||
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<math>w_0 = 1000\pi\ </math> | <math>w_0 = 1000\pi\ </math> | ||
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 10:06, 16 September 2013
Contents
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
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\ $
