Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Fast Fourier transform

A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa.

History, Applications & Research

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Fast Fourier transform. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

History

Definition

Algorithms

FFT algorithms specialized for real or symmetric data

Computational issues

Multidimensional FFTs

Other generalizations

Applications

Alternatives

Research areas

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Fast Fourier transform

Nodes143
Edges142
Triples170
Avg. degree1.99
Density0.013986
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Fast Fourier transform

Top relations

related to Further reading · 122
Fast Fourier transform → Academic Press, Acoustics, Alan, Algorithms, An Owner's Manual, Applications, Applied, Applied Mathematics, Archived, Audio, Audrey, Berlin, Berlin Heidelberg, Bibcode, Boca Raton, Boston, Brian, Briggs, Brigham, Burrus
related to External links · 20
Fast Fourier transform → Archived, Cooley, FFT, FFT Code, FFT Tutorial, Fourier, GPL-licensed, January, MIT's, Pascal, Polynomial Multiplication, Sound, Sparse Fast Fourier Transform, Thirty, Tukey, VB6, VBA, Vibration, Wayback Machine, Welaratna
related to Bounds on complexity and operation counts · 18
Fast Fourier transform → Burrus, CPU, DFT, DFTs, Duhamel, FFT, Following, Fourier, Frigo, Heideman, However, In, It, Johnson, Moreover, Omega, Shmuel Winograd, Theta

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

fft algorithm algorithms dft textstyle log fourier tukey transform cooley complexity displaystyle fast transforms data many real ffts time isbn

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
multiplications by 1instance ofoperations can be saved by eliminating trivial operations0.80text
leaving about 30 million operationsinstance ofoperations can be saved by eliminating trivial operations0.80text
the split-radix FFT have their own names as wellinstance ofand other variants0.80text
cache or CPU pipeline optimization.Following work by Shmuel Winogradinstance ofalthough actual performance on modern-day computers is determined by many other factors0.80text
astronomyinstance ofResearch areasBig FFTsWith the explosion of big data in fields0.80text
the need for 512K FFTs has arisen for certain interferometry calculationsinstance ofResearch areasBig FFTsWith the explosion of big data in fields0.80text
WMAPinstance ofThe data collected by projects0.80text
LIGO require FFTs of tens of billions of pointsinstance ofThe data collected by projects0.80text
MRIinstance ofApproximate FFTsFor applications0.80text
it is necessary to compute DFTs for nonuniformly spaced grid points and/or frequenciesinstance ofApproximate FFTsFor applications0.80text
Fast Fourier transformrelated to Bounds on complexity and operation countsFourier0.60section
Fast Fourier transformrelated to Bounds on complexity and operation countsIt0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.