Fourier Analysis
Produces the Fourier analysis of a data set by computing the Discrete Fourier Transform (DFT) of an input array of complex numbers using a couple of Fast Fourier Transform (FFT) algorithms.
For more information on Fourier analysis, refer to the corresponding Wikipedia article.
Input range has label: Mark when the first row or column of the input array is actually a label and not part of the data analysis.
Input Range 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.
Options:
Inverse: When checked, calculates the inverse Discrete Fourier Transform.
Polar: When checked, the results are in polar coordinates (magnitude, phase).
Minimum magnitude for polar form output (in dB): used only when output is in polar form. All frequency components with magnitude less than this value in decibels 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.
The source data for this example is the same of the FOURIER function page.
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Fourier Transform |
Fourier Transform |
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Input data range : $B$6:$C$40 |
Input data range : $B$6:$C$40 |
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Real |
Imaginary |
Magnitude |
Phase |
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17.1775578743134 |
3.88635177703826E-15 |
17.1775578743134 |
2.26245884628906E-16 |
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3.428868795359 |
2.37164790000189 |
4.16915518748944 |
0.605113892937279 |
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-6.80271615433369 |
-15.1345439297576 |
16.5931120359682 |
-1.99322000923881 |
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-1.605447356601 |
-5.08653060378972 |
5.33387802617444 |
-1.87652762269615 |
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0.395847917447356 |
-2.41926785527625 |
2.45143886917874 |
-1.40861048708919 |
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-1.49410383304833 |
-2.39148041275 |
2.81984482347817 |
-2.12922380028329 |
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0.87223579298981 |
-1.14394086206797 |
1.43853952829993 |
-0.919353665468368 |
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1.5332458505929 |
0.678159168870983 |
1.6765269746366 |
0.416434654153369 |
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0.450563708411459 |
0.22911248792634 |
0.505470263676592 |
0.470425948779898 |
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0.545106616940358 |
0.411028927740438 |
0.682704916689207 |
0.646077879418302 |
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2.22685996425193 |
-2.43092236748302 |
3.29670879167654 |
-0.829181229907427 |
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-1.61522859107175 |
-2.41682657284899 |
2.90689079338124 |
-2.15994697868441 |
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1.30245078290168 |
1.45443785733126 |
1.95237484175544 |
0.840472341525344 |
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1.57930628561185 |
-1.33862736591677 |
2.07029745895472 |
-0.70310180067089 |
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-1.07572227365276 |
-0.921557968003809 |
1.41649126309482 |
-2.43322886402899 |
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-0.055782417923803 |
-1.81336029451831 |
1.81421807837012 |
-1.60154853447151 |
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-0.577666040004067 |
1.38887243891951 |
1.50421564456836 |
1.96495487990047 |
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-0.826878282157686 |
-0.186591000796403 |
0.847669685126376 |
-2.91965280961949 |
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-0.826878282157715 |
0.186591000796416 |
0.847669685126408 |
2.91965280961948 |
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-0.577666040004051 |
-1.38887243891954 |
1.50421564456838 |
-1.96495487990045 |
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-0.055782417923785 |
1.81336029451832 |
1.81421807837012 |
1.6015485344715 |
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-1.07572227365276 |
0.921557968003802 |
1.41649126309482 |
2.433228864029 |
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1.57930628561187 |
1.33862736591678 |
2.07029745895474 |
0.703101800670888 |
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1.3024507829017 |
-1.45443785733125 |
1.95237484175543 |
-0.840472341525331 |
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-1.61522859107176 |
2.416826572849 |
2.90689079338125 |
2.15994697868441 |
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2.22685996425191 |
2.43092236748304 |
3.29670879167653 |
0.829181229907435 |
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0.545106616940365 |
-0.411028927740441 |
0.682704916689214 |
-0.646077879418299 |
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0.450563708411458 |
-0.229112487926344 |
0.505470263676594 |
-0.470425948779905 |
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1.53324585059292 |
-0.678159168870965 |
1.6765269746366 |
-0.416434654153355 |
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|
0.872235792989797 |
1.14394086206799 |
1.43853952829994 |
0.919353665468386 |
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-1.49410383304834 |
2.39148041275001 |
2.81984482347818 |
2.12922380028329 |
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0.395847917447327 |
2.41926785527626 |
2.45143886917875 |
1.4086104870892 |
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-1.60544735660102 |
5.08653060378972 |
5.33387802617445 |
1.87652762269616 |
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-6.80271615433379 |
15.1345439297575 |
16.5931120359682 |
1.99322000923882 |
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3.42886879535907 |
-2.37164790000194 |
4.16915518748952 |
-0.605113892937279 |
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