Fourier transform
nounEtymology Named after French mathematician and physicist Jean Baptiste Joseph Fourier, who initiated the study of what is now harmonic analysis.
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Business, Electrical, Electrical engineering, Electricity, Electromagnetism, Energy, Engineering, Mathematical analysis, Mathematics, Natural sciences, Physical sciences, Physics, Sciences 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.
Harmonic analysis
- 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.
3 more examples
- 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:
- 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.
- Derived terms
- inverse Fourier transform, continuous Fourier transform, discrete Fourier transform, fast Fourier transform, Fourier-transform infrared spectroscopy
- Hypernyms
- integral transform