Phrase guide

Fourier transform

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion.

Definition source: English Wiktionary via Wiktextract

Qualifier: harmonic analysis

Topics: business, electrical, electrical-engineering, electricity, electromagnetism, energy, engineering, mathematical-analysis, mathematics, natural-sciences, physical-sciences, physics, sciences

Examples

  • Fourier transforms are not limited to acting on functions of time, but the domain of the original function is commonly called the time domain.
  • The Fourier transform of a function of time is a complex function of frequency, whose magnitude (absolute value) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency.
  • 2005, Emmanuel Letellier, Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras, Springer, Lecture Notes in Mathematics 1859, page 1, The trigonometric sums of G^F are thus (up to a scalar) the Fourier transforms of the characteristic functions of the G^F!!-orbits of G^F.
  • 2012, David Brandwood, Fourier Transforms in Radar and Signal Processing, Artech House, 2nd Edition, page 1, The Fourier transform is a valuable theoretical technique, used widely in fields such as applied mathematics, statistics, physics, and engineering.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Named after French mathematician and physicist Jean Baptiste Joseph Fourier, who initiated the study of what is now harmonic analysis.

Across languages

Translations

18 source translations are retained for this English entry.

  • Catalan: transformada de Fourier — mathematics: a type of integral transform
  • Dutch: Fouriertransformatie — mathematics: a type of integral transform
  • Dutch: Fourier-transformatie — mathematics: a type of integral transform
  • Finnish: Fourier-muunnos — mathematics: a type of integral transform
  • French: transformation de Fourier — mathematics: a type of integral transform
  • Galician: transformada de Fourier — mathematics: a type of integral transform
  • German: Fouriertransformation — mathematics: a type of integral transform
  • German: Fourier-Transformation — mathematics: a type of integral transform
  • Greek: μετασχηματισμός Φουριέ (metaschimatismós Fourié) — mathematics: a type of integral transform
  • Italian: trasformata di Fourier — mathematics: a type of integral transform
  • Japanese: フーリエ変換 (Fūrie henkan) — mathematics: a type of integral transform
  • Persian: تبدیل فوریه (tabdil-e furiye) — mathematics: a type of integral transform
  • Polish: transformata Fouriera — mathematics: a type of integral transform
  • Portuguese: transformada de Fourier — mathematics: a type of integral transform
  • Romanian: tranformare Fourier — mathematics: a type of integral transform
  • Russian: преобразова́ние Фурье́ (preobrazovánije Furʹjé) — mathematics: a type of integral transform
  • Spanish: transformada de Fourier — mathematics: a type of integral transform
  • Swedish: Fouriertransform — mathematics: a type of integral transform