10/09 - Fourier Transform: Difference between revisions
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==Definitions== | ==Definitions== | ||
<math></math> | {| border="0" cellpadding="0" cellspacing="0" | ||
|- | |||
|<math>F[x(t)]\,\!</math> | |||
|<math>=X(f)\,\!</math> | |||
|<math>=\int_{-\infty}^{\infty} x(t) e^{-j2\pi ft}dt</math> | |||
|<math>=\left \langle x(t) \mid e^{j2\pi ft}\right \rangle</math> | |||
|- | |||
|<math>F^{-1}[x(t)]\,\!</math> | |||
|<math>=x(t)\,\!</math> | |||
|<math>=\int_{-\infty}^{\infty} X(f) e^{j2\pi ft}dt</math> | |||
|<math>=\left \langle X(f) \mid e^{-j2\pi ft}\right \rangle</math> | |||
|} |
Revision as of 14:53, 17 November 2008
Assuming the function is perodic with the period T | ||
Fourier Transform
Remember from 10/02 - Fourier Series
If we let
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