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fft

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====== Fast Fourier Transform (FFT) ====== | ====== Fast Fourier Transform (FFT) ====== | ||

- | Open table with initial data and use ''Analysis -> Fast Fourier Transform'' | + | Open Table or Figure or Plot with initial data and use ''Processing -> Fast Fourier Transform''[[wp>FFT]]. |

- | ===== 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 of calculation. |

- | MagicPlot uses 'to set the sign of the exponential phase factor of FFT. ((Most scientific applications uses the same sign conventions. But note, that the sign of exponential phase factor in Numerical Receipts in C, 2nd edition, p. 503 is the opposite)) | + | |

- | Here < | + | {{:|}} |

- | | + | |

- | ^ Normalize \\ Check Box ^ Forward Transform \\ (Signal-> | + | |

- | ^ Unchecked {k=1}{N}{c_k e^{−2 pi i k n {/} N}}</| <}{N}{C_k e^{2 pi i k n {/} N}}</ | + | |

- | ^ Checked | + | |

===== Parameters ===== | ===== Parameters ===== | ||

- | ^ Sampling Interval | ||

- | ^ Real \\ Imaginary | ||

- | ^ Forward \\ Inverse | ||

- | ^ Normalize forward transform | ||

- | ^ Center zero frequency | ||

+ | ^ 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]] |

fft.1272230713.txt.gz · Last modified: Sun Nov 8 12:20:32 2015 (external edit)

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