(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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===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> |
Revision as of 18:38, 26 September 2008
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} $
