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<math>\ x(t) = e^{-2|t|}cos(8t)</math> | <math>\ x(t) = e^{-2|t|}cos(8t)</math> | ||
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| + | <math>X(\omega) = \int_{-\infty}^{\infty} x(t) e^{-j\omega t} dt \!</math> | ||
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| + | <math> = \int_{-\infty}^{\infty} e^{-2|t|}cos(8t) e^{-j\omega t} dt \!</math> | ||
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| + | <math> = \int_{-\infty}^{0} e^{2|t|}cos(8t) e^{-j\omega t} dt \! + \int_{0}^{\infty} e^{-2|t|}cos(8t) e^{-j\omega t} dt \!</math> | ||
Revision as of 12:47, 8 October 2008
$ \ x(t) = e^{-2|t|}cos(8t) $
$ X(\omega) = \int_{-\infty}^{\infty} x(t) e^{-j\omega t} dt \! $
$ = \int_{-\infty}^{\infty} e^{-2|t|}cos(8t) e^{-j\omega t} dt \! $
$ = \int_{-\infty}^{0} e^{2|t|}cos(8t) e^{-j\omega t} dt \! + \int_{0}^{\infty} e^{-2|t|}cos(8t) e^{-j\omega t} dt \! $
