# MagicPlot Manual

Plotting and nonlinear fitting software

### Sidebar

fft

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# Fast Fourier Transform (FFT) (Pro edition only)

Open Table or Figure or Plot with initial data and use `Processing → Fast Fourier Transform` menu item to perform 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.

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 case evaluation time of the FFT algorithm is much less. MagicPlot uses jfftpack library (a Java version of fftpack).

## Formulas

### Discrete Fourier Transform Formulas

MagicPlot uses 'electrical engineering' convention to set the sign of the exponential phase factor of FFT as follows from the table below. 1)

Normalize Forward
Transform
Forward Transform
(Signal→Spectrum)
Inverse Transform
(Spectrum→Signal)
Unchecked
Checked

Here cn are complex signal components and Cn are complex spectrum components, n = 1…N.

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 `Normalize Forward Transform` and `Center Zero Frequency` check boxes identically for forward and inverse transforms.

### Amplitude and Phase Columns Formulas

Because of using atan2 function the phase is unwrapped and is in range (−ππ].

### Sampling Column Formulas

Sampling column contains frequency samples if forward transform is performed and time samples in case of inverse transform.

Center Zero
Frequency
Formula Sampling Column Values
Unchecked
Checked

Here Δt 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.

## Parameters

 Sampling Interval Sampling interval of original data Δt is used to compute the data in resulting sampling column. If `Get from` box is set, MagicPlot will calculate sampling interval as difference between two beginning 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. Columns with real and imaginary components of data. If your data is only real, select `` imaginary item Transform direction (here Inverse equals to Backward) Divide forward transform result by number of points N (see 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 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.
1)
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