Fourier transform

Definitions

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.

Equivalents

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.”

“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.”

“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.”

CEFR level