Fourier transform

plural Fourier transforms · alternative initialism FT

1. harmonic analysisbusinessA 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.

   Fourier transforms are not limited to acting on functions of time, but the domain of the original function is commonly called the time domain.

   4 more examples

   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

   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.