(New page: = Fourier series coefficients for CT signal = ===CT Signal=== :<math>\, x(t)=6sin(6t)</math> ===Fourier series coefficients=== :<math>x(t)=\sum_{k=-\infty}^\infty a_k e^{jk\omega_0 t}</mat...) |
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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"]] | ||
| + | ---- | ||
| + | |||
= Fourier series coefficients for CT signal = | = Fourier series coefficients for CT signal = | ||
===CT Signal=== | ===CT Signal=== | ||
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===Fourier series coefficients=== | ===Fourier series coefficients=== | ||
:<math>x(t)=\sum_{k=-\infty}^\infty a_k e^{jk\omega_0 t}</math><br><br> | :<math>x(t)=\sum_{k=-\infty}^\infty a_k e^{jk\omega_0 t}</math><br><br> | ||
| − | :<math>\, x(t)=6sin(6t) = 6\cdot\frac{e^{j6t}-e^{-j6t}}{2j}=3(e^{j6t}-e^{-j6t})</math><br><br> | + | :<math>\, x(t)=6sin(6t) = 6\cdot\frac{e^{j6t}-e^{-j6t}}{2j}=\frac{3(e^{j6t}-e^{-j6t})}{j}</math><br><br> |
| − | :<math>\, x(t)=3e^{j6t}-3e^{-j6t}</math><br><br> | + | :<math>\, x(t)=\frac{3e^{j6t}}{j}-\frac{3e^{-j6t}}{j}</math><br><br> |
| − | :<math>\, a_1 = 3\ ,\ a_{-1} = 3</math> | + | :<math>\, a_1 = \frac{3}{j}\ ,\ a_{-1} = \frac{-3}{j}</math> |
| + | |||
| + | ---- | ||
| + | [[Signals_and_systems_practice_problems_list|Back to Practice Problems on Signals and Systems]] | ||
Latest revision as of 10:57, 16 September 2013
Contents
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Fourier series coefficients for CT signal
CT Signal
- $ \, x(t)=6sin(6t) $
Fourier series coefficients
- $ x(t)=\sum_{k=-\infty}^\infty a_k e^{jk\omega_0 t} $
- $ \, x(t)=6sin(6t) = 6\cdot\frac{e^{j6t}-e^{-j6t}}{2j}=\frac{3(e^{j6t}-e^{-j6t})}{j} $
- $ \, x(t)=\frac{3e^{j6t}}{j}-\frac{3e^{-j6t}}{j} $
- $ \, a_1 = \frac{3}{j}\ ,\ a_{-1} = \frac{-3}{j} $
