Fourier analysis

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.

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Fourier analysis

(ˈfʊərɪˌeɪ)

(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]

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

Fou′rier anal`ysis

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

Fourier analysis - analysis of a periodic function into a sum of simple sinusoidal components

harmonic analysis

analysis - a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation

Translations

Fourier-Analyse

analisi di Fourier

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References in periodicals archive

Jerry, The Gibbs phenomenon in Fourier Analysis, Splines and Wavelet Approximations, Kluwer Academic Publ, London, UK, 1998.

Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function

Zhang, "Fourier analysis on trapezoids with curved sides," Indian Journal of Pure and Applied Mathematics, vol.

Approximation of Functions on a Square by Interpolation Polynomials at Vertices and Few Fourier Coefficients

cochisei, as well as the shape of the hybrid individuals, quantified by the elliptical Fourier analysis (Fig.

Tests of the role of sexual selection in genitalic divergence with mutiple hybrid clines

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 Pribram-Bohm hypothesis a topology of consciousness

The results of Fourier analysis studies can be summarized and visualized using principal component analysis (PCA).

Elliptic Fourier Analysis of Male Genitalia in Bombus (S. Lato) Latreille

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.

Return of the harmonic analyzer: an engineer highlights the genius of a mechanical computer

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.

Condition monitoring of power transformer using MEMS sensor

Application of elliptical Fourier analysis of otolith form as a tool for stock identification.

Southern flounder (Paralichthys letliostigma) stock structure inferred from otolith shape analysis

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.).

Fourier('s) analysis: "sonic" heat conduction and its cold calculation

Dunkl operators provide an essential tool to extend Fourier analysis on Euclidean spaces.

Dunkl transform of ([beta], [gamma])-Dunkl Lipschitz functions

Appendices hold background information on fatigue models, statistics and probability, Fourier analysis, finite element analysis, multibody system simulation mathematics, and load analysis software.

Guide to Load Analysis for Durability in Vehicle Engineering

Although Fourier Analysis (FA) has some inherent limitations in the analysis of the non-linear phenomena and some short duration transient signals.

Fault detection of washing machine with discrete wavelet methods/Skalbimo masinos defektu atskleidimas diskretiniais banginiais metodais