# Fourier analysis

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Related to Fourier analysis: Fourier series

## Fourier analysis

n.
The branch of mathematics concerned with the approximation of periodic functions by the Fourier series and with generalizations of such approximations to a wider class of functions.

## Fourier analysis

(ˈfʊərɪˌeɪ)
n
(Mathematics) the analysis of a periodic function into its simple sinusoidal or harmonic components, whose sum forms a Fourier series
[C19: named after Baron Jean Baptiste Joseph Fourier (1768–1830), French mathematician, Egyptologist, and administrator]

## Fou′rier anal`ysis

n.
the expression of any periodic function as a sum of sine and cosine functions, as in an electromagnetic wave function.
[1925–30; after J.B.J. Fourier]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 Fourier analysis - analysis of a periodic function into a sum of simple sinusoidal componentsharmonic analysisanalysis - a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation
Translations
Fourier-Analyse
References in periodicals archive ?
Jerry, The Gibbs phenomenon in Fourier Analysis, Splines and Wavelet Approximations, Kluwer Academic Publ, London, UK, 1998.
Zhang, "Fourier analysis on trapezoids with curved sides," Indian Journal of Pure and Applied Mathematics, vol.
cochisei, as well as the shape of the hybrid individuals, quantified by the elliptical Fourier analysis (Fig.
202) Three years after Wiener's (1948) publication of Cybernetics, David Bohm (1951) stressed the importance of Fourier's equations on the first page of his well-received 646-page textbook, Quantum, Theory, where he encouraged a familiarity with Fourier analysis for an ontological understanding of quantum phenomena:
The results of Fourier analysis studies can be summarized and visualized using principal component analysis (PCA).
The book, Albert Michelson's Harmonic Analyzer: A Visual Tour of a Nineteenth Century Machine That Performs Fourier Analysis, is available as a free PDF download at www.engineerguy.com/fourier.
Prony method is a technique for modeling time series data as a linear combination of exponentials and it extends Fourier analysis. It is a technique of analyzing signals to determine magnitude, damping, phase, and frequency information contained in the signal.
Application of elliptical Fourier analysis of otolith form as a tool for stock identification.
In its simplest form, Fourier analysis decomposes complex periodic functions (such as those perceived as "sound") into the sum of simple sine and cosine waves counted in cycles per second (hertz) (Fourier transform, n.d.).
Dunkl operators provide an essential tool to extend Fourier analysis on Euclidean spaces.
Appendices hold background information on fatigue models, statistics and probability, Fourier analysis, finite element analysis, multibody system simulation mathematics, and load analysis software.
Although Fourier Analysis (FA) has some inherent limitations in the analysis of the non-linear phenomena and some short duration transient signals.

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