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| − | <math>x(t)= | + | <math>x(t)=e^{-3t} u(t-3) u(t+3) </math> |
<math>X(w) = \int^{\infty}_{- \infty}x(t)e^{-jwt} dt</math> | <math>X(w) = \int^{\infty}_{- \infty}x(t)e^{-jwt} dt</math> | ||
| − | <math>= \int^{\infty}_{- \infty} | + | <math>= \int^{\infty}_{- \infty} e^{-3t} u(t-3) u(t+3) e^{-jwt} dt</math> |
| − | <math>= \int^{ | + | <math>= \int^{3}_{-3} e^{-(3 + jw)t} dt</math> |
| − | <math>[ | + | <math>[\frac{e^{-(3 + jw)t}}{-(3 + jw)}]_{-3}^{3}</math> |
Revision as of 09:39, 7 October 2008
$ x(t)=e^{-3t} u(t-3) u(t+3) $
$ X(w) = \int^{\infty}_{- \infty}x(t)e^{-jwt} dt $
$ = \int^{\infty}_{- \infty} e^{-3t} u(t-3) u(t+3) e^{-jwt} dt $
$ = \int^{3}_{-3} e^{-(3 + jw)t} dt $
$ [\frac{e^{-(3 + jw)t}}{-(3 + jw)}]_{-3}^{3} $
