FOURIER
Computes the Discrete Fourier Transform [DFT] of an input array of complex numbers using a couple of Fast Fourier Transform (FFT) algorithms. The function is an array formula.
FOURIER(Array, GroupedByColumns, Inverse, Polar, MinimumMagnitude)
Array is a 2 x N or N x 2 range representing an array of complex number to be transformed, where N is the length of the array. The array represents the real and imaginary parts of the data.
GroupedByColumns is a logical (TRUE or FALSE, 1 or 0) argument. When TRUE the array is grouped by columns where the first column contains the real part of the complex number and the second columns contains the imaginary part of the complex number. When FALSE, the first row contains the real part of the complex number and the second row contains the imaginary part of the complex number. If there is only 1 column (row), the input sequence is treated as purely real.
Inverse is an optional logical (TRUE or FALSE, 1 or 0) argument. When TRUE, calculates the inverse Discrete Fourier Transform. The default value is FALSE.
Polar: is an optional logical (TRUE or FALSE, 1 or 0) argument. Indicates whether the final output is in polar coordinates (magnitude, phase). This argument is optional and the default value is FALSE.
MinimumMagnitude: used only if Polar=TRUE. All frequency components with magnitude less than MinimumMagnitude will be suppressed with a zero magnitude-phase entry. This is very useful when looking at the magnitude-phase spectrum of a signal because there is always some very tiny amount of rounding error when doing FFT algorithms and results in incorrect non-zero phase for non-existent frequencies. By providing a suitable value to this parameter, these non-existent frequency components can be suppressed. By default the value of MinimumMagnitude is 0.0, and no suppression is done by default.
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Group By Columns |
TRUE |
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Polar |
FALSE |
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Inverse |
FALSE |
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Formula |
{=FOURIER(B6:C40,B1,B2,B3,0)} |
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Source Array |
Transformed Array |
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Real |
Imaginary |
Real |
Imaginary |
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0.392555411592569 |
0 |
17.1775578743134 |
3.88635177703826E-015 |
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1.20843701681219 |
0 |
3.428868795359 |
2.37164790000189 |
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0.851477676762644 |
0 |
-6.80271615433369 |
-15.1345439297576 |
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1.78534651907738 |
0 |
-1.605447356601 |
-5.08653060378972 |
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1.77946506138316 |
0 |
0.395847917447356 |
-2.41926785527625 |
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1.51890060220168 |
0 |
-1.49410383304833 |
-2.39148041275 |
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1.04694666137238 |
0 |
0.87223579298981 |
-1.14394086206797 |
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0.83110083951399 |
0 |
1.5332458505929 |
0.678159168870983 |
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1.23006228455127 |
0 |
0.450563708411459 |
0.22911248792634 |
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0.133409796396031 |
0 |
0.545106616940358 |
0.411028927740438 |
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0.130471655802496 |
0 |
2.22685996425193 |
-2.43092236748302 |
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0.386478761838145 |
0 |
-1.61522859107175 |
-2.41682657284899 |
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-0.703398287742919 |
0 |
1.30245078290168 |
1.45443785733126 |
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|
-0.899115309693977 |
0 |
1.57930628561185 |
-1.33862736591677 |
|
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-0.124045510064504 |
0 |
-1.07572227365276 |
-0.921557968003809 |
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-0.513553513012611 |
0 |
-0.0557824179238028 |
-1.81336029451831 |
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-0.613559196487517 |
0 |
-0.577666040004067 |
1.38887243891951 |
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0.32607259491689 |
0 |
-0.826878282157686 |
-0.186591000796403 |
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0.0316297814625926 |
0 |
-0.826878282157715 |
0.186591000796416 |
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0.52298725899815 |
0 |
-0.577666040004051 |
-1.38887243891954 |
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0.436798031445888 |
0 |
-0.0557824179237846 |
1.81336029451832 |
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|
0.846212627320418 |
0 |
-1.07572227365276 |
0.921557968003802 |
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|
0.913061096906024 |
0 |
1.57930628561187 |
1.33862736591678 |
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|
1.2666287534781 |
0 |
1.3024507829017 |
-1.45443785733125 |
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1.6653650481107 |
0 |
-1.61522859107176 |
2.416826572849 |
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1.36582636202864 |
0 |
2.22685996425191 |
2.43092236748304 |
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1.46722190894756 |
0 |
0.545106616940365 |
-0.411028927740441 |
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0.66120489728397 |
0 |
0.450563708411458 |
-0.229112487926344 |
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0.701534531762234 |
0 |
1.53324585059292 |
-0.678159168870965 |
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0.65869368245062 |
0 |
0.872235792989797 |
1.14394086206799 |
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|
0.287522455580069 |
0 |
-1.49410383304834 |
2.39148041275001 |
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-0.409911360506096 |
0 |
0.395847917447327 |
2.41926785527626 |
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|
-0.583168875679498 |
0 |
-1.60544735660102 |
5.08653060378972 |
|
|
-0.799684083650078 |
0 |
-6.80271615433379 |
15.1345439297575 |
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-0.621417306845244 |
0 |
3.42886879535907 |
-2.37164790000194 |
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