Show pageOld revisionsBacklinksBack to top This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Discrete Fourier Transform ====== $\hat{a}_k = \sum^{N-1}_{j=0} e^{-2\pi * i * \frac{jk}{N}} * \hat{a}_j$ Komplexe Exponentialfunktion: $e^{-x} = \cos x - i \sin x$ $X[k] = \sum^{N-1}_{n=0} X[n] \cos(\omega_k * n) - i \sum^{N-1}_{n=0} X[n] \sin(\omega_k * n)$ $\omega_k= \frac{2 \pi k}{N}$ Multiplikation und Summierung => Korrelation Maß für Anwesendheit von Cosinus (Reelle Zahlen) / Sinus Wellen (Imaginäre Zahlen) k => Anzahl der Zyklen. Positive Zahlen => time_series/fft.txt Last modified: 2014/08/12 00:02by phreazer