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fft [Mon Jun 14 19:01:02 2010] Alexander |
fft [Thu Jan 14 17:14:11 2021] (current) Alexander |
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Open Table or Figure or Plot with initial data and use '' | Open Table or Figure or Plot with initial data and use '' | ||
- | Fast Fourier transform algorithm | + | Fast Fourier transform algorithm |
- | MagicPlot uses the algorithm of FFT that does not require the number of points //N// to be the integer power of 2. Though the evaluation time of the FFT algorithm is much less if //N// is the integer power of 2. MagicPlot uses [[http://www.netlib.org/ | + | {{:fft.png?nolink|}} |
- | {{:fft1.png|FFT of table columns dialog}} {{:fft2.png|FFT of curves dialog}} | + | ===== Parameters ===== |
+ | |||
+ | ^ Sampling Interval | ||
+ | ^ Real, \\ Imaginary | ||
+ | ^ Forward / \\ Inverse | ||
+ | ^ 1/N in forward transform | ||
+ | ^ Center zero frequency | ||
+ | |||
+ | ===== Algorithm ===== | ||
+ | |||
+ | MagicPlot uses the algorithm | ||
- | ===== 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 1///N// multiplier. | + | \\ |
- | Note: If you expect to get the original data when doing a inverse FFT of forward FFT set the '' | + | ^ 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 ==== | ==== Amplitude and Phase Columns Formulas ==== | ||
- | <m>Amplitude_n | + | <m>A_n = sqrt{{Re_n}^2 + {Im_n}^2}, |
- | Because of using [[wp> | + | 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 Δ//t// is given sampling interval of initial data. | + | ^ 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 ==== | ==== Missing Values in the Original Data ==== | ||
- | Fourier transform implies that the original samples are uniformly distributed in time (for forward transform) | + | Fourier transform implies that the original samples are uniformly distributed in time (for forward 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 middle or in beginning of original data columns are treated as zeros, the result of Fourier transform may be incorrect. | ||
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* Missing values in the end of the column are ignored. | * Missing values in the end of the column are ignored. | ||
- | ===== Parameters | + | ===== See Also ===== |
- | ^ Sampling Interval | + | |
- | ^ Real, \\ Imaginary | + | |
- | ^ Forward / \\ Inverse | + | |
- | ^ Normalize forward transform | + | |
- | ^ Center zero frequency | + |