Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revisionLast revisionBoth sides next revision | ||
| time_series:fft [2014/08/11 21:18] – phreazer | time_series:fft [2014/08/11 21:25] – phreazer | ||
|---|---|---|---|
| Line 2: | Line 2: | ||
| $\hat{a}_k = \sum^{N-1}_{j=0} e^{-2\pi * i * \frac{jk}{N}} * \hat{a}_j$ | $\hat{a}_k = \sum^{N-1}_{j=0} e^{-2\pi * i * \frac{jk}{N}} * \hat{a}_j$ | ||
| - | |||
| - | $e^-i\dots$ | ||
| Komplexe Exponentialfunktion: | Komplexe Exponentialfunktion: | ||
| $e^{-x} = \cos x - i \sin x$ | $e^{-x} = \cos x - i \sin x$ | ||
| - | $X[k] = \sum^{N-1}_{j=0} X[j] \cos(\omega_k * j) - i \sum^{N-1}_{j=0} X[j] \sin(\omega_k * j)$ | + | $X[k] = \sum^{N-1}_{n=0} X[n] \cos(\omega_k * n) - i \sum^{N-1}_{n=0} X[n] \sin(\omega_k * n)$ |
| + | |||
| + | $\omega_k= \frac{2 \pi k}{N}$ | ||
| Multiplikation und Summierung => Korrelation | Multiplikation und Summierung => Korrelation | ||
| + | Maß für Anwesendheit von Cosinus (Reelle Zahlen) / Sinus Wellen (Imaginäre Zahlen) | ||
| - | + | k => Anzahl der Zyklen. | |