# MagicPlot Manual

Plotting and nonlinear fitting software

fft

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 fft [Mon Feb 28 12:43:08 2011]Alexander fft [Thu Jan 14 17:14:11 2021]Alexander Both sides previous revision Previous revision Thu Jan 14 17:14:11 2021 Alexander Sun Nov 8 12:21:24 2015 external editMon May 12 18:27:15 2014 Alexander Mon May 12 18:05:47 2014 Alexander Tue Jun 4 00:49:15 2013 Alexander Mon Jun 3 15:42:02 2013 Alexander Thu May 30 12:07:37 2013 Alexander Mon Feb 28 12:43:08 2011 Alexander Mon Feb 28 12:40:50 2011 Alexander Fri Nov 5 12:32:12 2010 Gray Sun Oct 31 22:25:18 2010 Gray Tue Oct 26 10:59:32 2010 Alexander Tue Oct 26 10:57:03 2010 Alexander Tue Oct 26 10:05:33 2010 Alexander Thu Oct 7 13:17:06 2010 Alexander Tue Jul 6 10:34:36 2010 Alexander Tue Jul 6 10:20:14 2010 Alexander Sun Jun 27 15:38:14 2010 Gray Sun Jun 27 14:48:46 2010 Gray Sun Jun 27 14:21:38 2010 Gray Sat Jun 26 21:46:59 2010 Alexander Sat Jun 26 20:50:05 2010 Alexander Mon Jun 14 19:01:28 2010 Alexander Mon Jun 14 19:01:02 2010 Alexander Mon Jun 14 18:45:47 2010 Alexander Mon Jun 14 18:32:14 2010 Alexander Thu Jun 10 09:22:21 2010 Alexander Thu May 20 19:57:08 2010 Alexander Wed May 12 18:53:06 2010 Alexander Wed May 12 18:51:01 2010 Alexander Wed May 5 10:04:06 2010 Alexander Wed May 5 10:02:13 2010 Alexander Wed May 5 10:01:41 2010 Alexander Next revision Previous revision Thu Jan 14 17:14:11 2021 Alexander Sun Nov 8 12:21:24 2015 external editMon May 12 18:27:15 2014 Alexander Mon May 12 18:05:47 2014 Alexander Tue Jun 4 00:49:15 2013 Alexander Mon Jun 3 15:42:02 2013 Alexander Thu May 30 12:07:37 2013 Alexander Mon Feb 28 12:43:08 2011 Alexander Mon Feb 28 12:40:50 2011 Alexander Fri Nov 5 12:32:12 2010 Gray Sun Oct 31 22:25:18 2010 Gray Tue Oct 26 10:59:32 2010 Alexander Tue Oct 26 10:57:03 2010 Alexander Tue Oct 26 10:05:33 2010 Alexander Thu Oct 7 13:17:06 2010 Alexander Tue Jul 6 10:34:36 2010 Alexander Tue Jul 6 10:20:14 2010 Alexander Sun Jun 27 15:38:14 2010 Gray Sun Jun 27 14:48:46 2010 Gray Sun Jun 27 14:21:38 2010 Gray Sat Jun 26 21:46:59 2010 Alexander Sat Jun 26 20:50:05 2010 Alexander Mon Jun 14 19:01:28 2010 Alexander Mon Jun 14 19:01:02 2010 Alexander Mon Jun 14 18:45:47 2010 Alexander Mon Jun 14 18:32:14 2010 Alexander Thu Jun 10 09:22:21 2010 Alexander Thu May 20 19:57:08 2010 Alexander Wed May 12 18:53:06 2010 Alexander Wed May 12 18:51:01 2010 Alexander Wed May 5 10:04:06 2010 Alexander Wed May 5 10:02:13 2010 Alexander Wed May 5 10:01:41 2010 Alexander Wed May 5 09:58:52 2010 Alexander Tue May 4 18:39:46 2010 Alexander Fri Apr 30 09:41:56 2010 Alexander Fri Apr 30 09:41:10 2010 Alexander Wed Apr 28 13:36:54 2010 Alexander Wed Apr 28 10:49:24 2010 Alexander Mon Apr 26 13:03:27 2010 Alexander Mon Apr 26 11:27:16 2010 Alexander Mon Apr 26 09:21:14 2010 Alexander Mon Apr 26 09:09:27 2010 Alexander Mon Apr 26 02:15:00 2010 Alexander Mon Apr 26 01:46:13 2010 Alexander Mon Apr 26 01:45:28 2010 Alexander Mon Apr 26 01:40:59 2010 Alexander Mon Apr 26 01:25:13 2010 Alexander Mon Apr 26 00:58:15 2010 Alexander created Line 1: Line 1: - ====== Fast Fourier Transform (FFT) (Pro edition only) ====== + ====== Fast Fourier Transform (FFT) ====== Open Table or Figure or Plot with initial data and use ''Processing -> Fast Fourier Transform'' menu item to perform [[wp>FFT]]. Open Table or Figure or Plot with initial data and use ''Processing -> Fast Fourier Transform'' menu item to perform [[wp>FFT]]. 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. 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 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://www.netlib.org/fftpack|jfftpack]] library (a Java version of fftpack). + {{:fft.png?nolink|}} - | {{:fft1.png|FFT of table columns dialog}} | {{:fft2.png|FFT of curves dialog}} | + ===== Parameters ===== + + ^ Sampling Interval  | Sampling interval of original data Δ//t// is used to compute the data in resulting sampling column. MagicPlot calculates sampling interval as a difference between second and first values in ''Sampling'' column. You can set sampling interval manually in ''Sampling Interval'' field. \\ Note that using of discrete Fourier transform implies that the samples in your original data are equally spaced in time/frequency, i.e. the sampling interval is constant. If the sampling interval is varying or real and/or imaginary data contains empty cells in the middle, the result of discrete Fourier transform will be incorrect.  | + ^ Real, \\ Imaginary  | Columns with real and imaginary components of data. \\ If your data is purely real, select '''' imaginary item  | + ^ Forward / \\ Inverse  | Transform direction (here ''Inverse'' also equals to ''Backward'') | + ^ 1/N in forward transform  | Divide forward transform result by number of points //N// (see formulas table). If your original data is real, you may want to additionally multiply the result by 2 to get the true amplitudes of real signal. Also referred as ''Normalize'' in some other applications.  | + ^ Center zero frequency  | If selected, after forward Fourier transform the two parts of spectrum will be rearranged so that the lower frequency components are in the center; the opposite rearrangement of spectrum will be done before inverse transform if any. Also referred as ''Shift FFT'' in some other applications. | + + ===== 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://www.netlib.org/fftpack|jfftpack]] library (a Java version of fftpack). - ===== Formulas ===== ==== Discrete Fourier Transform Formulas ==== ==== Discrete Fourier Transform Formulas ==== By default MagicPlot uses 'electrical engineering' convention to set the sign of the exponential phase factor of FFT: forward transform is computed using factor ''-1''. Most scientific applications use factor ''-1'' in forward transform as MagicPlot does by default. But note that the sign of exponential phase factor in Numerical Receipts in C, 2nd edition, p. 503 and in MATLAB package in forward transform is ''+1''. By default MagicPlot uses 'electrical engineering' convention to set the sign of the exponential phase factor of FFT: forward transform is computed using factor ''-1''. Most scientific applications use factor ''-1'' in forward transform as MagicPlot does by default. But note that the sign of exponential phase factor in Numerical Receipts in C, 2nd edition, p. 503 and in MATLAB package in forward transform is ''+1''. Line 48: Line 57: * 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  | Sampling interval of original data Δ//t// is used to compute the data in resulting sampling column. If ''Get from''  box is set, MagicPlot will calculate sampling interval as a difference between two first values from given column. You can set sampling interval manually by checking ''Set manually'' box. \\ Note that using of discrete Fourier transform implies that the samples in your original data are equally spaced in time/frequency, i.e. the sampling interval is constant. If the sampling interval is varying or real and/or imaginary data contains empty cells in the middle, the result of discrete Fourier transform will be incorrect.  | + * [[processing]] - ^ Real, \\ Imaginary  | Columns with real and imaginary components of data. \\ If your data is purely real, select ''''  imaginary item  | + - ^ Forward / \\ Inverse  | Transform direction (here Inverse equals to Backward) | + - ^ 1/N in forward transform  | Also referred as 'Normalize' in some applications. Divide forward transform result by number of points //N// (see formulas table). If your original data is real, you may want to additionally multiply the result by 2 to get the true amplitudes of real signal  | + - ^ Center zero frequency  | If selected, after forward Fourier transform the two parts of spectrum will be rearranged so that the lower frequency components are in the center; the opposite rearrangement of spectrum will be done before inverse transform if any.  | +