| Line 11: | Line 11: | ||
:<math>x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \,</math> | :<math>x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \,</math> | ||
| − | :<math>e^{j2 \pi t}\,</math> | + | :<math>x(t) = e^{j2 \pi t}\,</math> |
Revision as of 17:23, 7 October 2008
The formula of the inverse transform is:
- $ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} X(jw)e^{jwt}dw \, $
Suppose we have $ 2 \pi \delta(w - 2\pi) $ (From the 'not so easy' question in class)
Substituting that into the formula:
- $ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} 2 \pi \delta(w - 2\pi) e^{jwt}dw \, $
- $ x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \, $
- $ x(t) = e^{j2 \pi t}\, $
