MagicPlot Manual

Plotting and nonlinear fitting software

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Table of Contents

Fast Fourier Transform (FFT)

Open table with initial data and use Analysis → Fast Fourier Transform menu item to perform FFT.

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 C_n = sum{k=1}{N}{c_k e^{−2 pi i k n {/} N}} c_n = 1/N sum{k=1}{N}{C_k e^{2 pi i k n {/} N}}
Checked C_n = 1/N sum{k=1}{N}{c_k e^{−2 pi i k n {/} N}} c_n = sum{k=1}{N}{C_k e^{2 pi i k n {/} N}}

Here c_n are complex signal components and C_n are complex spectrum components, n = 1...N.

Abs_n = sqrt{{Re_n}^2 + {Im_n}^2},~~ Phase_n = atan2(Im_n,~ Re_n)

Sampling Column Formulas

Center Zero
Frequency
Sampling Column Values
Unchecked 0,~ 1/{N Delta t},~ 2/{N Delta t},~ ... ~{N−1}/{N Delta t}
Checked {−{N{/}2}/{N Delta t}},~ ...~ 0,~ ... ~{N{/}2−1}/{N Delta t}

Here Delta t is given sampling interval of initial data.

Parameters

Sampling Interval Sampling interval Delta t 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.
Real
Imaginary
Columns with real and imaginary components of data.
If your data is only real, select <all zeros> imaginary item
Forward
Inverse
Transform direction
Normalize forward transform Divide forward transform result by number of points N
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.
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
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fft.1272233700.txt.gz · Last modified: Sun Nov 8 12:20:32 2015 (external edit)