Fourier analysis


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Related to Fourier analysis: Fourier series

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.

Fou·ri·er a·nal·y·sis

(fūr-ē-ā' ă-nal'i-sis)
A mathematical approximation of a function as the sum of periodic functions (sine waves) of different frequencies; used in reconstruction of magnetic resonance images and computed tomographs and analysis of any kind of signal for its frequency content.

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

Fourier analysis

The mathematical breakdown of waveforms into simple sine wave constituents. Any complex waveform consists of sine waves of different frequencies: the slowest (fundamental) frequency and harmonics thereof (these are frequencies which are odd multiples of the fundamental frequency). It is used in analysis and reconstruction of waveforms as, for example, analysing the spatial frequency components of a visual image. Syn. Fourier transform. See contrast sensitivity.
References in periodicals archive ?
Applying the Fourier analysis with h = 1, n = 16 on a n x n grid to (4.
2001) A First Course in Wavelets with Fourier Analysis, Prentice Hall.
Fourier analysis is, however, only exact for linear operators with constant (or frozen) coefficients.
On June 4, 2009, I received from Abdul a draft copy of his manuscript entitled Wavelets, Detailed Treatment with Basic Fourier Analysis, [B 6].
According to Wavelets: A Key Advance in Signal Processing Technology, a Futuretech report from Technical Insights, wavelet analysis offers considerable advantages over traditional Fourier analysis by being able to handle signals of short duration.
The normalized Fourier correlation coefficient, NFCC can be built from the Fourier analysis, described (Grierson, 2006) by
faster and more accurate Fourier analysis calculation and to continue
The chief clock architect at a microelectronics company, Xiu draws on number theory and Fourier analysis to investigate how to improve the relationship between time and number in very large integrated circuits.
Fourier analysis has been around for a couple of centuries, say Boggess and Narcowich (both mathematics, Texas A&M U.
Another result in both complex function theory and classical Fourier analysis which is needed here is the Paley-Wiener theorem (see, e.
From the recommendations provided by literature the best way to correlate pure time series is the Fourier analysis method (Pytharouli, S, 2004; Pytharouliand & Stiros, 2005).
The textbook and accompanying software is significantly more detailed than typical introductions to partial differential equations, they say, and provide examples on setting up physical problems as mathematical ones, solving partial differential equations under different types of boundary conditions, working with special functions, and carrying out a Fourier analysis using these functions.