Fourier transform en · NOUN
Etymology
Named after French mathematician and physicist Jean Baptiste Joseph Fourier, who initiated the study of what is now harmonic analysis.
Meanings
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(qualifier:harmonic analysis) 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.
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.
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.
Since a separate integration is needed to give each point of the transformed function, the process would become extremely tedious if it were to be attempted manually and many ingenious devices have been invented for preforming Fourier transforms mechanically, electrically, acoustically and optically.
2002, J. F. James, A Student's Guide to Fourier Transforms, 2nd edition, Cambridge University Press, page 116:Fourier transforms are not limited to acting on functions of time, but the domain of the original function is commonly called the time domain.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Fourier transforms | Number=Plur | lexicographic | |
| FT | alternative, initialism | lexicographic |
Deriveds
fast Fourier transform · Fourier-transform infrared spectroscopy · discrete Fourier transform · inverse Fourier transform · continuous Fourier transform
Hypernyms
Translations (19)
el μετασχηματισμός Φουριέ (mathematics: a type of integral transform) · ja フーリエ変換 (mathematics: a type of integral transform) · pt transformada de Fourier (mathematics: a type of integral transform) · ca transformada de Fourier (mathematics: a type of integral transform) · nl Fouriertransformatie (mathematics: a type of integral transform) · fr transformation de Fourier (mathematics: a type of integral transform) · ro tranformare Fourier (mathematics: a type of integral transform) · it trasformata di Fourier (mathematics: a type of integral transform) · de Fourier-Transformation (mathematics: a type of integral transform) · es transformada de Fourier (mathematics: a type of integral transform) · fa تبدیل فوریه (mathematics: a type of integral transform) · gl transformada de Fourier (mathematics: a type of integral transform) · nl Fourier-transformatie (mathematics: a type of integral transform) · pl transformata Fouriera (mathematics: a type of integral transform) · he הַתְמָרַת פוּרְיֶה (mathematics: a type of integral transform) · fi Fourier-muunnos (mathematics: a type of integral transform) · de Fouriertransformation (mathematics: a type of integral transform) · ru преобразова́ние Фурье́ (mathematics: a type of integral transform) · sv Fouriertransform (mathematics: a type of integral transform)