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.

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note

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


Datos

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.

Opciones:

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.

Exemplos

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

Tresformada de Fourier

Tresformada de Fourier

Estaya de datos d'entrada: $B$6:$C$40

Estaya de datos d'entrada: $B$6:$C$40

Real

Imaxinariu

Magnitú

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