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<math> X(w) = \int_{-\infty}^{1}e^{(t-1)}e^{-jwt}dt+\int_{1}^{\infty}e^{-(t-1)}e^{-jwt}dt</math><br><br> | <math> X(w) = \int_{-\infty}^{1}e^{(t-1)}e^{-jwt}dt+\int_{1}^{\infty}e^{-(t-1)}e^{-jwt}dt</math><br><br> | ||
<math> X(w) = \int_{-\infty}^{1}e^{-1}e^{(1-jw)t}dt+\int_{1}^{\infty}e^{1}e^{(1+jw)t}dt</math><br><br> | <math> X(w) = \int_{-\infty}^{1}e^{-1}e^{(1-jw)t}dt+\int_{1}^{\infty}e^{1}e^{(1+jw)t}dt</math><br><br> | ||
| − | <math> X(w) = {\left.\frac{e^{-1}e^{(1-jw)t}}{1-jw}\right]_{\infty}^{0}}}}+{\left.\frac{e^{1}e^{-(1+jw)t}}{1+jw}\right]_{\infty}^{0}}}} | + | <math> X(w) = {\left.\frac{e^{-1}e^{(1-jw)t}}{1-jw}\right]_{\infty}^{0}}}}+{\left.\frac{e^{1}e^{-(1+jw)t}}{1+jw}\right]_{\infty}^{0}}}}</math><br><br> |
</math> | </math> | ||
Revision as of 16:55, 7 October 2008
$ x(t) = e^{-|t-1|} \, $
$ X(w) = \int_{-\infty}^{\infty}e^{-|t-1|}e^{-jwt}dt $
$ X(w) = \int_{-\infty}^{1}e^{(t-1)}e^{-jwt}dt+\int_{1}^{\infty}e^{-(t-1)}e^{-jwt}dt $
$ X(w) = \int_{-\infty}^{1}e^{-1}e^{(1-jw)t}dt+\int_{1}^{\infty}e^{1}e^{(1+jw)t}dt $
$ X(w) = {\left.\frac{e^{-1}e^{(1-jw)t}}{1-jw}\right]_{\infty}^{0}}}}+{\left.\frac{e^{1}e^{-(1+jw)t}}{1+jw}\right]_{\infty}^{0}}}} $
</math>
