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When | When | ||
| − | <math> t-2 < 0 \rightarrow | + | <math> t-2 < 0 \rightarrow x_1(t) = e^{3t-6} </math> |
and when, | and when, | ||
| − | <math> t-2 >0 \rightarrow | + | <math> t-2 >0 \rightarrow x_2(t) = e^{-3t-6} </math> |
So, we can then compute the Fourier series by adding the integrals of each diferent case. | So, we can then compute the Fourier series by adding the integrals of each diferent case. | ||
| − | <math>\ \mathcal{X}(\omega)=\int_{-\infty}^{\infty} | + | <math>\ \mathcal{X}(\omega)=\int_{-\infty}^{\infty}x_1(t)e^{-j\omega t}\,dt\ + \int_{-\infty}^{\infty}x_2(t)e^{-j\omega t}\,dt\</math> |
Revision as of 16:27, 8 October 2008
$ x(t) = e^{-3|t-2|} $
Noticing that there is an absolute value, we can proceed to divide in tow cases.
When
$ t-2 < 0 \rightarrow x_1(t) = e^{3t-6} $
and when,
$ t-2 >0 \rightarrow x_2(t) = e^{-3t-6} $
So, we can then compute the Fourier series by adding the integrals of each diferent case.
$ \ \mathcal{X}(\omega)=\int_{-\infty}^{\infty}x_1(t)e^{-j\omega t}\,dt\ + \int_{-\infty}^{\infty}x_2(t)e^{-j\omega t}\,dt\ $
