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.

To access this command...

Choose Data - Statistics - Fourier Analysis

For more information on Fourier analysis, refer to the corresponding Wikipedia article.

Data

Input Range: The reference of the range of the data to analyze.

Results to: The reference of the top left cell of the range where the results will be displayed.

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.

Grouped By

Select whether the input data has columns or rows layout.

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.

Examples

The source data for this example is the same of the FOURIER function page.

 Fourier Transform Fourier Transform Input data range : \$B\$6:\$C\$40 Input data range : \$B\$6:\$C\$40 Real Imaginary Magnitude Phase 17.1775578743134 3.88635177703826E-15 17.1775578743134 2.26245884628906E-16 3.428868795359 2.37164790000189 4.16915518748944 0.605113892937279 -6.80271615433369 -15.1345439297576 16.5931120359682 -1.99322000923881 -1.605447356601 -5.08653060378972 5.33387802617444 -1.87652762269615 0.395847917447356 -2.41926785527625 2.45143886917874 -1.40861048708919 -1.49410383304833 -2.39148041275 2.81984482347817 -2.12922380028329 0.87223579298981 -1.14394086206797 1.43853952829993 -0.919353665468368 1.5332458505929 0.678159168870983 1.6765269746366 0.416434654153369 0.450563708411459 0.22911248792634 0.505470263676592 0.470425948779898 0.545106616940358 0.411028927740438 0.682704916689207 0.646077879418302 2.22685996425193 -2.43092236748302 3.29670879167654 -0.829181229907427 -1.61522859107175 -2.41682657284899 2.90689079338124 -2.15994697868441 1.30245078290168 1.45443785733126 1.95237484175544 0.840472341525344 1.57930628561185 -1.33862736591677 2.07029745895472 -0.70310180067089 -1.07572227365276 -0.921557968003809 1.41649126309482 -2.43322886402899 -0.055782417923803 -1.81336029451831 1.81421807837012 -1.60154853447151 -0.577666040004067 1.38887243891951 1.50421564456836 1.96495487990047 -0.826878282157686 -0.186591000796403 0.847669685126376 -2.91965280961949 -0.826878282157715 0.186591000796416 0.847669685126408 2.91965280961948 -0.577666040004051 -1.38887243891954 1.50421564456838 -1.96495487990045 -0.055782417923785 1.81336029451832 1.81421807837012 1.6015485344715 -1.07572227365276 0.921557968003802 1.41649126309482 2.433228864029 1.57930628561187 1.33862736591678 2.07029745895474 0.703101800670888 1.3024507829017 -1.45443785733125 1.95237484175543 -0.840472341525331 -1.61522859107176 2.416826572849 2.90689079338125 2.15994697868441 2.22685996425191 2.43092236748304 3.29670879167653 0.829181229907435 0.545106616940365 -0.411028927740441 0.682704916689214 -0.646077879418299 0.450563708411458 -0.229112487926344 0.505470263676594 -0.470425948779905 1.53324585059292 -0.678159168870965 1.6765269746366 -0.416434654153355 0.872235792989797 1.14394086206799 1.43853952829994 0.919353665468386 -1.49410383304834 2.39148041275001 2.81984482347818 2.12922380028329 0.395847917447327 2.41926785527626 2.45143886917875 1.4086104870892 -1.60544735660102 5.08653060378972 5.33387802617445 1.87652762269616 -6.80271615433379 15.1345439297575 16.5931120359682 1.99322000923882 3.42886879535907 -2.37164790000194 4.16915518748952 -0.605113892937279