Fourier series

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Related to Fourier modes: Fourier series, Fourier theorem

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
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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
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References in periodicals archive ?
Then construct a subset [OMEGA](K) of the phase space (the set of possible configurations of the Fourier modes) so that all points in [OMEGA](K) possess the desired decay properties.
Therefore, we choose the admittance function (shown in (13)) with medium filling ratio and low contrast, so 31 Fourier modes are sufficient to give a harsh but accurate results.
Figure 2 shows the diffraction efficiency for the 0-th order reflection versus the truncation order, i.e., the upper index M of the Fourier modes in one periodic direction.
In other words, terms of the series with low spatial frequencies (small numbers n) determine the behavior of their sum (3) in the distance of the slot edges, whereas the field asymptotics at these edges will be determined by higher-order Fourier modes. Thus, the standard technique of infinite sum truncation makes possible correct simulation of diffraction fields in the distance of the slot edges, but it does not provide adequate evaluation of their edge asymptotic behavior.
According to these studies branching depends on undulating shapes "(described as static Fourier modes) at high curvatures and thus allows the development of regularly branched fibers with the spacing between the branches depending on the peaks of the longest wavelength Fourier mode.