Noun
Fourier transform (plural Fourier transforms)
(mathematical analysis, harmonic analysis, physics, electrical engineering) 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.
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.
Accordingly, the technique of "Fourier transform spectroscopy" can be used both for measuring emission spectra (for example, the emission spectrum of a star), and absorption spectra (for example, the absorption spectrum of a liquid). Source: Internet
A data-processing technique called Fourier transform turns this raw data into the desired result (the sample's spectrum): Light output as a function of infrared wavelength (or equivalently, wavenumber ). Source: Internet
Alternatively, the entire wavelength range is measured using a Fourier transform instrument and then a transmittance or absorbance spectrum is generated using a dedicated procedure. Source: Internet
A DCT is similar to a Fourier transform in the sense that it produces a kind of spatial frequency spectrum. Source: Internet
An example of a rapidly falling function is for any positive n, λ, β. To study the Fourier transform, it is best to consider complex-valued test functions and complex-linear distributions. Source: Internet
All of the basic properties listed above hold for the n-dimensional Fourier transform, as do Plancherel's and Parseval's theorem. Source: Internet