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<math>[\frac{e^{-(3 + jw)t}}{-(3 + jw)}]_{-3}^{3}</math> | <math>[\frac{e^{-(3 + jw)t}}{-(3 + jw)}]_{-3}^{3}</math> | ||
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| + | <math>\frac{e^{-(9 + 3jw)}}{-(3 + jw)} - \frac{e^{(9 + 3jw)}}{-(3 + jw)}</math> | ||
Revision as of 10:43, 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} $
$ \frac{e^{-(9 + 3jw)}}{-(3 + jw)} - \frac{e^{(9 + 3jw)}}{-(3 + jw)} $
