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 ?
The Fast Fourier Transform provides a general picture of temporal behavior of wind speed and the associated wind direction is also considered for ventilation design purpose.
Liu, "Pitt's inequality and the uncertainty principle associated with the quaternion fourier transform," Journal of Mathematical Analysis and Applications, vol.
Solgaard, "Micromachined Fourier transform spectrometer on silicon optical bench platform," in The 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005.
(4) Taking the inverse Fourier transform of [H.sub.w](f), obtained transform function h(t) is windowed by the same time window [t1 t2], but, to compensate the filter delay used in step 3, time window is shifted by the same filter delay and then [h.sub.w](t) is obtained.
Equations (5) and (6) imply that the 2-D AOAs are decoupled and obtained by Fourier transform, given the continuous phase distribution around a circular aperture.
Wang, "The poisson sum formulae associated with the fractional fourier transform," Signal Processing, vol.
In this subsection, we introduce the quaternionic windowed Fourier transform (QWFT) and obtain the relationship between the QAF-LCT and QWFT.
The task to find a shift between two images is converted by the phase correlation to the task of finding the only nonzero point in a matrix (computation using the discrete Fourier transform).
We combined the matrix form of this discrete Laplace transform with a generalized fast Fourier transform in a purely algebraic fashion, where we used the decomposition of the Laplace transform explicitly and a small number of generalized FFTs as black box.
Method for eliminating zero spectrum in Fourier transform profilometry, Optics and Lasers in Engineering, 43(11), 1267-1276.
We first define the Fourier transform of certain discrete functions.
Allen, "Short term spectral analysis, synthesis, and modification by discrete Fourier transform," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.

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