Fourier series

An infinite series whose terms are constants multiplied by sine and cosine functions and that can, if uniformly convergent, approximate a wide variety of functions.

[After Baron Jean Baptiste Joseph Fourier.]

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 series

(Mathematics) an infinite trigonometric series of the form a0 + a1cos x + b1sin x + a2cos 2x + b2sin 2x + …, where a0, a1, b1, a2, b2 … are the Fourier coefficients. It is used, esp in mathematics and physics, to represent or approximate any periodic function by assigning suitable values to the coefficients

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

Fou′rier se`ries

an infinite series that approximates a given function on a specified domain by using linear combinations of sines and cosines.

[1875–80; see Fourier analysis]

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Noun

Fourier series - the sum of a series of trigonometric expressions; used in the analysis of periodic functions

series - (mathematics) the sum of a finite or infinite sequence of expressions

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References in periodicals archive

Then the equation becomes time-harmonic and the solution can be approximated with a truncated Fourier series expansion.

Parallel Solution Methods and Preconditioners for Evolution Equations

Given a function of class Lp let us consider its conjugate trigonometric Fourier series

Pointwise approximation of modified conjugate functions by matrix operators of their Fourier series

This new approach is developed in terms of double Fourier series and can take account of a finite dislocation core size, which is not possible with the integral formalism.

Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches

The solution of the resulting integral equation is reduced to the solution of a truncated linear system by using the truncated Fourier series. Finally, the solution of Dirichlet problem has the form of the real part of the Cauchy integral.

The Approximate Solution of 2D Dirichlet Problem in Doubly Connected Domains

One method was proposed to fulfill these requirements, which assumes the displacements in the geometrical z-direction and can be represented using Fourier series. Exploiting its orthogonal properties, the problem of such a class can thus be simplified into a series of 2D solutions.

Application of Linear Viscoelastic Properties in Semianalytical Finite Element Method with Recursive Time Integration to Analyze Asphalt Pavement Structure

He defined T-convolution, a different type of classical convolution, for [P'.sub.T] and discussed Fourier series of [P'.sub.T].

Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support

The next section describes the Fourier series estimator of f([theta]) that is shown to be equivalent to the circular kernel density estimator (2) in a limiting sense when wrapped Cauchy kernel is employed.

Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle

The idea of the method is to measure the positions and gravitational torques of different joints through designing Fourier series as excitation trajectories.

Nonlinear Friction and Dynamical Identification for a Robot Manipulator with Improved Cuckoo Search Algorithm

Let [M.sub.N](f, x) be the truncated modified Fourier series

Optimal Rational Approximations by the Modified Fourier Basis

In order to obtain the Elliptic Fourier Descriptor of the boundary curve, Fourier series expansion is first carried out, and it can be expanded by 1D Fourier series.

Stability Evaluation of Fault Diagnosis Model Based on Elliptic Fourier Descriptor

A frame for a Hilbert space firstly emerged in the work on nonharmonic Fourier series owing to Duffin and Schaeffer [1], which has made great contributions to various fields because of its nice properties; the reader can examine the papers [2-12] for background and details of frames.

A New Inequality for Frames in Hilbert Spaces