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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"]] | ||
| + | ---- | ||
Defines the Fourier series of a periodic ct signal as | Defines the Fourier series of a periodic ct signal as | ||
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<math>x(t)=6sin(2\pi t) + 4cos(4\pi t)</math> | <math>x(t)=6sin(2\pi t) + 4cos(4\pi t)</math> | ||
| − | <math>=6*\frac{e^{2j\pi t} - e^{-2j\pi t}}{2j}</math> | + | <math>=6*\frac{e^{2j\pi t} - e^{-2j\pi t}}{2j} + 4 *\frac{e^{4j\pi t} + e^{-4j\pi t}}{2} </math> |
| + | |||
| + | <math>=3*\frac{e^{2j\pi t} - e^{-2j\pi t}}{j}+ 2 * (e^{4j\pi t}+e^{-4j\pi t})</math> | ||
| + | |||
| + | <math>a_1 = \frac{3}{j}</math> | ||
| + | |||
| + | <math>a_2 = \frac{-3}{j}</math> | ||
| + | |||
| + | <math>a_3 = 2</math> | ||
| + | |||
| + | <math>a_4=2</math> | ||
| + | |||
| + | else | ||
| + | |||
| + | <math>a_k = 0</math> | ||
| + | |||
| + | <math>w_0 = \pi</math> | ||
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 10:03, 16 September 2013
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Defines the Fourier series of a periodic ct signal as
$ x(t) = \sum_{k=-\infty}^\infty a_k e^{jkw_0t} $
I set a example as
$ x(t)=6sin(2\pi t) + 4cos(4\pi t) $
$ =6*\frac{e^{2j\pi t} - e^{-2j\pi t}}{2j} + 4 *\frac{e^{4j\pi t} + e^{-4j\pi t}}{2} $
$ =3*\frac{e^{2j\pi t} - e^{-2j\pi t}}{j}+ 2 * (e^{4j\pi t}+e^{-4j\pi t}) $
$ a_1 = \frac{3}{j} $
$ a_2 = \frac{-3}{j} $
$ a_3 = 2 $
$ a_4=2 $
else
$ a_k = 0 $
$ w_0 = \pi $
