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<math>= \frac{3j - 7}{2} e^{j2\pi t} + \frac{5j - 9}{2} e^{-j2\pi t}</math> | <math>= \frac{3j - 7}{2} e^{j2\pi t} + \frac{5j - 9}{2} e^{-j2\pi t}</math> | ||
| + | |||
| + | <math>\frac{3j}{2} e^{j 2\pi t} - \frac{7}{2} e^{j 2\pi t} + \frac{5j}{2} e^{-j 2\pi t} - \frac{9}{2} e^{-j 2\pi t}</math> | ||
Revision as of 07:32, 8 October 2008
$ X(w) = \pi \delta (w - 2 \pi)(3j - 7) + \pi \delta (w + 2 \pi) (5j - 9) $
$ x(t) = \frac{1}{2 \pi} \int^{\infty}_{- \infty} X(w) e^{jwt} dw $
$ = \frac{1}{2 \pi} \int^{\infty}_{- \infty} [ \pi \delta (w - 2 \pi)(3j - 7) + \pi \delta (w + 2 \pi) (5j - 9)] e^{jwt} dw $
$ = \frac{3j - 7}{2}\int^{\infty}_{- \infty}\delta (w -2\pi) e^{jwt} dw + \frac {5j - 9}{2}\int^{\infty}_{- \infty}\delta (w + 2\pi) e^{jwt} dw $
$ = \frac{3j - 7}{2} e^{j2\pi t} + \frac{5j - 9}{2} e^{-j2\pi t} $
$ \frac{3j}{2} e^{j 2\pi t} - \frac{7}{2} e^{j 2\pi t} + \frac{5j}{2} e^{-j 2\pi t} - \frac{9}{2} e^{-j 2\pi t} $
