# Fourier series

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Related to Fourier series: Fourier transform

## Fourier series

n.
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.]

## Fourier series

n
(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

## Fou′rier se`ries

n.
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]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 Fourier series - the sum of a series of trigonometric expressions; used in the analysis of periodic functionsseries - (mathematics) the sum of a finite or infinite sequence of expressions
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Such a decomposition is now known as a Fourier series, and has had wide-ranging applications across mathematics and wider science, for example in signal processing and in solving complicated differential equations.
Then the equation becomes time-harmonic and the solution can be approximated with a truncated Fourier series expansion.
Given a function of class Lp let us consider its conjugate trigonometric 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.
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.
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.
He defined T-convolution, a different type of classical convolution, for [P'.sub.T] and discussed Fourier series of [P'.sub.T].
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.
The idea of the method is to measure the positions and gravitational torques of different joints through designing Fourier series as excitation trajectories.
Let [M.sub.N](f, x) be the truncated modified Fourier series
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.
A frame for a Hilbert space firstly emerged in the work on nonharmonic Fourier series owing to Duffin and Schaeffer , 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.

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