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 (FT)

[fo̅o̅ryā′]
Etymology: Jean B.J. Fourier, French mathematician, 1768-1830; L, transformare, to change form
a mathematical procedure that separates out the frequency components of a signal from its amplitudes as a function of time, or vice versa.

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 ?
Each Fourier transform F(Q) equals the volume integral [8] of the respective [rho](r)exp(-iQ * r), Q denoting the wave vector transfer.
is inadequate for a Fourier transform since (for solids) E(t) [is not equal to] 0 as t [right arrow] [infinity].
He then proceeds to the vector space, Sturm-Liouville problems, convolution and the delta function ("a splat and a spike"), Fourier transforms and integrals, local frequency analysis and wavelets.
Dual channel 16K point Fast Fourier Transforms with the appropriate filtering;
Early chapters on general theory cover areas including Fourier analysis, the mathematics of complex numbers, Fourier transforms, and differential equations.
in Electrical Engineering from Johns Hopkins University, and is the author of the definitive book The Handbook of Real-Time Fast Fourier Transforms.
IPs that Lattice intends to make available include popular functions such as Finite Impulse Response (FIR) Filters and Fast Fourier Transforms (FFTs).
AirNet brings over 10 years of broadband, software-defined radio product expertise utilizing orthogonal frequency division multiplexing ("OFDM") technology implementing Fast Fourier Transforms ("FFT") to the WiMAX Forum.
The library, initially available with a FORTRAN interface, is comprised of a full implementation of optimized Level 1, 2 and 3 Basic Linear Algebra Subroutines (BLAS), Linear Algebra Package (LAPACK) as well as Fast Fourier Transforms (FFTs) in single-, double-, single-complex and double-complex data types.
0 is a collection of reusable linear algebra, Fast Fourier Transforms and vector math and statistical functions with a common applications programming interface.
The library, to be made available with both FORTRAN and C interfaces, will be comprised of a full implementation of Level 1, 2 and 3 Basic Linear Algebra Subroutines (BLAS), Linear Algebra Package (LAPACK) as well as Fast Fourier Transforms (FFTs) in single-, double-, single-complex and double-complex data types.
His topics include a classification of signals, linear systems, practical Fourier transforms, discrete signals, and introductory communications.

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