This shows you the differences between two versions of the page.
Next revision | Previous revision | ||
fft [Mon Apr 26 00:58:15 2010] Alexander created |
fft [Thu Jan 14 17:14:11 2021] (current) Alexander |
||
---|---|---|---|
Line 1: | Line 1: | ||
====== Fast Fourier Transform (FFT) ====== | ====== Fast Fourier Transform (FFT) ====== | ||
- | Open table with initial data and use '' | + | Open Table or Figure or Plot with initial data and use '' |
- | ===== Formulas ===== | + | Fast Fourier transform algorithm computes discrete Fourier transform exactly and is used to considerably speed up the calculations.\\ Note that FFT is not an approximate method |
- | MagicPlot uses ' | + | |
- | Here < | + | {{:fft.png? |
- | ^ Normalize \\ Check Box ^ Forward Transform | + | ===== Parameters ===== |
- | ^ Unchecked | + | |
- | ^ Checked | + | |
+ | ^ Sampling Interval | ||
+ | ^ Real, \\ Imaginary | ||
+ | ^ Forward / \\ Inverse | ||
+ | ^ 1/N in forward transform | ||
+ | ^ Center zero frequency | ||
+ | |||
+ | ===== Algorithm ===== | ||
+ | |||
+ | MagicPlot uses the algorithm of FFT that does not necessarily require the number of points //N// to be an integer power of 2, though in such a case evaluation is faster. MagicPlot uses [[http:// | ||
+ | |||
+ | ==== Discrete Fourier Transform Formulas ==== | ||
+ | By default MagicPlot uses ' | ||
+ | |||
+ | ^ Factor −1 (Default) | ||
+ | ^ 1/N in forward \\ transform | ||
+ | ^ Checked \\ (Default) | ||
+ | ^ Unchecked | ||
+ | |||
+ | \\ | ||
+ | |||
+ | ^ Factor +1 (Scientific) | ||
+ | ^ 1/N in forward \\ transform | ||
+ | ^ Checked \\ (Default) | ||
+ | ^ Unchecked | ||
+ | |||
+ | |||
+ | Here // | ||
+ | |||
+ | Note: if you expect to get the original data when doing an inverse FFT of forward FFT, set the '' | ||
+ | |||
+ | ==== Amplitude and Phase Columns Formulas ==== | ||
+ | < | ||
+ | |||
+ | Because of using '' | ||
+ | |||
+ | ==== Sampling Column Formulas ==== | ||
+ | Sampling column contains frequency samples if forward transform is performed and time samples in case of inverse transform. | ||
+ | ^ Center zero \\ frequency | ||
+ | ^ Unchecked | ||
+ | ^ Checked | ||
+ | Here Δ//t// is given sampling interval of initial data (time for FFT and frequency for IFFT), //n// = 1...//N//. | ||
+ | |||
+ | ==== Missing Values in the Original Data ==== | ||
+ | Fourier transform implies that the original samples are uniformly distributed in time (for forward transform) or frequency (for inverse transform). | ||
+ | |||
+ | * Missing values in the middle or in beginning of original data columns are treated as zeros, the result of Fourier transform may be incorrect. | ||
+ | |||
+ | * Missing values in the end of the column are ignored. | ||
+ | |||
+ | ===== See Also ===== | ||
+ | * [[processing]] |