(New page: ===Useful Info=== <math>x(t)=\sum_{k=-\infty}^{\infty}a_ke^{jk\omega_0t}</math> <math>a_k=\frac{1}{T}\int_0^Tx(t)e^{-jk\omega_0t}dt</math>. :Let :<math> x(t) = 2sin(2\pi t) + cos(\pi t)....) |
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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"]] | ||
| + | ---- | ||
| + | |||
===Useful Info=== | ===Useful Info=== | ||
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:<math> a_1 = \frac{1}{j} </math> | :<math> a_1 = \frac{1}{j} </math> | ||
:<math> a_2 = \frac{1}{2} </math> | :<math> a_2 = \frac{1}{2} </math> | ||
| + | |||
| + | :<math> \omega_0 = \frac{2\pi}{T} = \frac{2\pi}{2\pi} = 1 </math> | ||
| + | |||
| + | :else | ||
| + | :<math> a_k = 0 </math> | ||
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 09:53, 16 September 2013
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Useful Info
$ x(t)=\sum_{k=-\infty}^{\infty}a_ke^{jk\omega_0t} $
$ a_k=\frac{1}{T}\int_0^Tx(t)e^{-jk\omega_0t}dt $.
- Let
- $ x(t) = 2sin(2\pi t) + cos(\pi t). $
Solution
- $ x(t) = 2\frac{e^{2 \pi jt}+e^{-2 \pi jt}}{2j} + \frac{e^{\pi jt}+e^{-\pi jt}}{2} $
- $ x(t) = \frac{1}{j}(e^{2 \pi jt} + e^{-2 \pi jt}) + \frac{1}{2}(e^{\pi jt}+e^{-\pi jt}) $
- $ a_1 = \frac{1}{j} $
- $ a_2 = \frac{1}{2} $
- $ \omega_0 = \frac{2\pi}{T} = \frac{2\pi}{2\pi} = 1 $
- else
- $ a_k = 0 $
