10/09 - Fourier Transform: Difference between revisions
Jump to navigation
Jump to search
Line 65: | Line 65: | ||
|<math>=\int_{-\infty}^{\infty}x(\lambda) \int_{-\infty}^{\infty}e^{j2\pi f(t-\lambda)} df d\lambda</math> |
|<math>=\int_{-\infty}^{\infty}x(\lambda) \int_{-\infty}^{\infty}e^{j2\pi f(t-\lambda)} df d\lambda</math> |
||
|<math>=\int_{-\infty}^{\infty}x(\lambda) \delta(t-\lambda) d\lambda</math> |
|<math>=\int_{-\infty}^{\infty}x(\lambda) \delta(t-\lambda) d\lambda</math> |
||
|<math>=x(t)\,\!</math> |
|||
|- |
|||
| |
|||
|<math>=\int_{-\infty}^{\infty}\left [ \int_{-\infty}^{\infty} x(\lambda) e^{-j\omega\lambda}d\lambda\right ]e^{j\omega t} \frac{1}{2\pi}d\omega </math> |
|||
|<math>=\int_{-\infty}^{\infty}x(\lambda) \left [ \frac{1}{2\pi} \int_{-\infty}^{\infty} e^{j(t-\omega) \lambda}d\omega\right ] d\lambda</math> |
|||
|<math>=\int_{-\infty}^{\infty}x(\lambda) \delta(t-\omega) d\lambda</math> |
|||
|<math>=x(t)\,\!</math> |
|<math>=x(t)\,\!</math> |
||
|} |
|} |
Revision as of 17:53, 17 November 2008
Assuming the function is perodic with the period T | ||
Fourier Transform
Remember from 10/02 - Fourier Series
If we let
Remember | ||