(New page: CT Periodic Signal : <math>x(t) = \cos(2\pi t) + \sin(3\pi t)\,</math> <math>= \frac{e^{2j\pi t}}{2} + \frac{e^{-2j\pi t}}{2} + \frac{e^{3j\pi t}}{2j} - \frac{e^{-3j\pi t}}{2j} \,</math...) |
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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"]] | ||
| + | ---- | ||
CT Periodic Signal : | CT Periodic Signal : | ||
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<math>a_k = 0 , k \neq 2,-2,3,-3\,</math> | <math>a_k = 0 , k \neq 2,-2,3,-3\,</math> | ||
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| + | Reference -* [[HW4.1 Wei Jian Chan_ECE301Fall2008mboutin]] | ||
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 11:09, 16 September 2013
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
CT Periodic Signal :
$ x(t) = \cos(2\pi t) + \sin(3\pi t)\, $
$ = \frac{e^{2j\pi t}}{2} + \frac{e^{-2j\pi t}}{2} + \frac{e^{3j\pi t}}{2j} - \frac{e^{-3j\pi t}}{2j} \, $
$ \omega_o \, $ = $ \pi \, $
Coefficients of signal:
$ a_2 = \frac{1}{2}\, $
$ a_{-2} = \frac{1}{2}\, $
$ a_{3} = \frac{1}{2j}\, $
$ a_{-3} = -\frac{1}{2j}\, $
Since
$ x(t) = \sum^{\infty}_{k = -\infty} a_k e^{jk\pi t}\, $ where
$ a_2 = a_{-2} = \frac{1}{2}\, $
$ a_{3} = -a_{-3}\, $
$ a_k = 0 , k \neq 2,-2,3,-3\, $
Reference -* HW4.1 Wei Jian Chan_ECE301Fall2008mboutin
