Fourier transform

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Fou·ri·er a·nal·y·sis

(fūr-ē-ā'),
a mathematical approximation of a function as the sum of periodic functions (sine and/or cosine waves) of different frequencies; a method of converting a function of time or space into a function of frequency; used in reconstruction of images in computed tomography and magnetic resonance imaging in radiology and in analysis of any kind of signal for its frequency content.

Fourier transform

A computational procedure used by MRI scanners to analyse and separate amplitude and phases of individual frequency components of the complex time varying signal, which allows spatial information to be reconstructed from the raw data.

Fou·ri·er trans·form

(fūr-ē-ā' trans'fōrm)
A mathematical technique of dividing a time-varying function or signal into components at different frequencies, giving the phase and amplitude of each; used in computed tomography and magnetic resonance image reconstruction transformation.

Fourier,

J.B.J., French mathematician and administrator, 1768-1830.
Fourier analysis - used in reconstruction of images in computed tomography and magnetic resonance imaging in radiology and in analysis of any kind of signal for its frequency content. Synonym(s): Fourier law; Fourier transform
Fourier law - Synonym(s): Fourier analysis
Fourier transform - Synonym(s): Fourier analysis
References in periodicals archive ?
FAST FOURIER TRANSFORMATION OF EMITTED NOISES FROM WELDING MACHINES AND THEIR CLASSIFICATION WITH ACOUSTIC METHOD
(k)-(o) and (p)-(t) Intensity distributions of POVs after the Fourier transformation of (a)-(e) for P = 1.3 [mm] and P = 0.7 [mm], respectively.
[M.sub.S] exploits discrete fast Fourier transformation routines to evaluate the even and odd spectra [[??].sub.E,S] and [[??].sub.O,S] conditionally on the spectral limits [f.sub.L] = 0 GHz and [f.sub.U] = 3747.4 GHz (Nyquist assumptions), the spectral increment [[DELTA].sub.f] = 3.66 GHz, vanishing shift [delta]x, and the zero-path difference [x.sub.0] = - 5.118 mm.
The Z([z.sup.2][??]) given in (17) is just the [PHI](z [right arrow] 0) ~ [z.sup.[DELTA]] modes of the bulk solution, while the Fourier transformation of (19) is a linear combination of the [PHI](z [right arrow] 0) ~ [z.sup.[DELTA]] modes and the [PHI](z [right arrow] 0) ~ [z.sup.d-[DELTA]] modes [14] which regulate the divergence of (18).
Similar to the Cooley-Turkey Fast Fourier Transformation (FFT) algorithm, the planned algorithm can generate the next higher-rider DCT from two identical lower-order DCTs.
Prime95 performs multiplications using really large numbers using an algorithm called Fast Fourier Transformation. Prime95 uses one of the most efficient methods of running these calculations and when one specific length of FFT is used (768k), Skylake processors freeze up.
However, in reality, this requires advanced ambiguity analysis, cross correlation, Fourier transformation, and intelligent error detection."
In digital computing, fast Fourier transformation is the time-efficient algorithmic implementation of this operation, allowing for a kind of real-time speech analysis that only computing can achieve.
Let us consider various ways of shifting the phase-frequency response characteristic for digital FIR-filters on the basis of frequency sampling method and the sliding discrete complex Fourier transformation. We will get mathematical models for digital filters without the shift of the phase-frequency response characteristic [7] and digital filters with the shift of the phase-frequency response characteristic.
The NMR detector coil then quantifies this signal as "amplitude." Fourier transformation of the FID signal results in an NMR spectrum, whereby, the measured frequency and amplitude provide detailed structure of the atoms and molecules in the analyzed specimen.
One possibility to obtain information about internal structure of the particles is the indirect Fourier transformation (IFT) technique, resulting in the pair density distribution function, PDDF.
Using the Laplace transformation and Fourier transformation, a stretched semi-infinite string subjected to a moving force with a constant acceleration was considered by Sagartz and Forrestal [6].

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