Fourier series

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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.]
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

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
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


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]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.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
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
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The Fourier expansion of the Poincare series for [[GAMMA].sup.+.sub.0](p).
A note on the non-vanishing of Poincare series for the Fricke group [[GAMMA].sup.+.sub.0](p)
In addition, they appear in numerical analysis, for instance in the context of the modulated Fourier expansion [9, 17], adiabatic integrators [17, 25] as well as Lawson-type Runge-Kutta methods [24].
ASYMPTOTIC CONSISTENT EXPONENTIAL-TYPE INTEGRATORS FOR KLEIN-GORDON-SCHRODINGER SYSTEMS FROM RELATIVISTIC TO NON-RELATIVISTIC REGIMES
To estimate the time derivative term in the unsteady flow governing equations, the time-marching method employs a finite difference method, while time-spectral methods used in this study apply a discrete Fourier expansion and Chebyshev polynomials.
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Caption: Figure 1: The graph of [absolute value of ([R.sub.N](f,x))] on [-0.7,0.7] for N = 64 while approximating (53) by the modified Fourier expansion (2).
Optimal Rational Approximations by the Modified Fourier Basis
First, we define a continuous curve c(t) in order to explain a Fourier Expansion (see Figure 8).
Stability Evaluation of Fault Diagnosis Model Based on Elliptic Fourier Descriptor
Since the stiffness is periodically time-varying with the mesh frequency, its analytical formulation can be obtained by means of a Fourier expansion [15]:
Coupled Bending-Torsional Nonlinear Vibration and Bifurcation Characteristics of Spiral Bevel Gear System
where [delta](x) is a continuous periodic function of period 1, mean zero, small amplitude and Fourier expansion
Descents after maxima in compositions
If the boundary is closed, it can be performed by the Fourier expansion in the two coordinate directions to calculate Fourier coefficients.
Arabidopsis growth simulation using image processing technology
The concept of Fourier expansion is involved in the resistive boundary condition.
CHARACTERIZATION AND INVESTIGATION OF COMPOSITE RESISTIVE GRATING
If the covariance function of X has the following Fourier expansion
Levy-based error prediction in circular systematic sampling

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