(New page: Let x(t)= <math>cos(t)</math> Then <math>X(\omega) = \int_{-\infty}^{\infty}x(t)e^{-j\omega t}dt</math> <math>X(\omega) = \int_{-\infty}^{\infty}cos(2t)e^{-j\omega t}dt \,</math> <mat...) |
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<math>X(\omega) = \int_{-\infty}^{\infty}x(t)e^{-j\omega t}dt</math> | <math>X(\omega) = \int_{-\infty}^{\infty}x(t)e^{-j\omega t}dt</math> | ||
| − | <math>X(\omega) = \int_{-\infty}^{\infty}cos( | + | <math>X(\omega) = \int_{-\infty}^{\infty}cos(t)e^{-j\omega t}dt</math> |
| − | <math>X(\omega) = \int_{-\infty}^{\infty}\frac{1}{2}(e^{jt}+e^{-jt})e^{-j\omega t}dt \ | + | <math>X(\omega) = \int_{-\infty}^{\infty}\frac{1}{2}(e^{jt}+e^{-jt})e^{-j\omega t}dt</math> |
| + | |||
| + | <math>X(\omega) = \frac{1}{2}(\int_{-\infty}^{\infty}e^{jt(1-\omega}+int_{-\infty}^{\infty}e^{-jt(1+\omega)})</math> | ||
Revision as of 07:49, 8 October 2008
Let x(t)= $ cos(t) $
Then
$ X(\omega) = \int_{-\infty}^{\infty}x(t)e^{-j\omega t}dt $
$ X(\omega) = \int_{-\infty}^{\infty}cos(t)e^{-j\omega t}dt $
$ X(\omega) = \int_{-\infty}^{\infty}\frac{1}{2}(e^{jt}+e^{-jt})e^{-j\omega t}dt $
$ X(\omega) = \frac{1}{2}(\int_{-\infty}^{\infty}e^{jt(1-\omega}+int_{-\infty}^{\infty}e^{-jt(1+\omega)}) $
