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====== 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 '' |
- | MagicPlot uses the algorithm of FFT that does not require the number of points < | + | 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 |
- | {{:fft1.png|}} | + | {{:fft.png?nolink|}} |
+ | |||
+ | ===== Parameters ===== | ||
+ | |||
+ | ^ 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:// | ||
- | ===== Formulas ===== | ||
==== Discrete Fourier Transform Formulas ==== | ==== Discrete Fourier Transform Formulas ==== | ||
- | MagicPlot uses ' | + | By default |
- | ^ | + | ^ |
- | ^ | + | ^ 1/N in forward |
- | ^ | + | ^ |
- | Here < | + | ^ |
- | The only difference is in the sign of exponential phase factor and < | + | \\ |
- | Note: If you expect to get the original data when doing a inverse FFT of forward | + | ^ Factor +1 (Scientific) |
+ | ^ 1/N in forward | ||
+ | ^ Checked \\ (Default) | ||
+ | ^ Unchecked | ||
- | ==== Abs and Phase Columns Formulas ==== | ||
- | < | ||
- | Because of using [[wp> | + | 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 Formulas ==== | ||
- | ^ Center | + | Sampling column contains frequency samples if forward transform is performed and time samples in case of inverse transform. |
- | ^ Unchecked | + | ^ Center |
- | ^ Checked | + | ^ Unchecked |
- | Here < | + | ^ Checked |
+ | Here Δ//t// is given sampling interval of initial data (time for FFT and frequency for IFFT), //n// = 1...//N//. | ||
- | ===== Parameters ===== | + | ==== Missing Values in the Original Data ==== |
- | ^ Sampling Interval | + | Fourier transform implies that the original |
- | ^ Real, \\ Imaginary | + | |
- | ^ Forward / \\ Inverse | + | * Missing values in the middle |
- | ^ Normalize forward transform | + | |
- | ^ Center zero frequency | + | |
+ | |||
+ | ===== See Also ===== | ||
+ | * [[processing]] |