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<math>x(t) = \frac{1}{2 \pi} \int^{\infty}_{- \infty} X(w) e^{jwt} dw</math> | <math>x(t) = \frac{1}{2 \pi} \int^{\infty}_{- \infty} X(w) e^{jwt} dw</math> | ||
| − | <math>\frac{1}{2 \pi} \int^{\infty}_{- \infty} [ \pi \delta (w - 2 \pi)(3j - 7) + \pi \delta (w + 2 \pi) (5j - 9)] e^{jwt} dw</math> | + | <math> = \frac{1}{2 \pi} \int^{\infty}_{- \infty} [ \pi \delta (w - 2 \pi)(3j - 7) + \pi \delta (w + 2 \pi) (5j - 9)] e^{jwt} dw</math> |
| − | <math>\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</math> | + | <math> = \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</math> |
Revision as of 10:41, 7 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 $
