# 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.]

## 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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In the field of the quantification of designing elements, (McGarva and Mullineux, 1993) made a research on the closed planar curve that expressed by the Fourier coefficient and proposed the theoretical method that using harmonic wave to represent the closed curve to make quantitative analysis on the design.
p], and of Y(t) Fourier coefficient [absolute value of [[?
nk] is the Fourier coefficient of order n x k in the Fourier expansion of the covariance function of X.
Note that because of symmetry, the value of a Fourier coefficient [?
mn] (kf, cosh [xi], cos [phi]) is given by Equation (9) for j = 3, whereas the associated mnth Fourier coefficient [d.
Success depends on the fortunate circumstance that when the quotient of the aspect ratio divided by the number of field periods is near 2, then the value of the Fourier coefficient [B.
can be regarded as the Fourier coefficient of G(t, s) as a function of s.
As a third feature, a Fourier coefficient at a certain frequency is considered.
theta], [phi]) of every grid can be calculated efficiently by applying 2-D IFFT to the zeros padded Fourier coefficient matrix [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The following has been derived for the strain cosine Fourier coefficient of the diffraction line profile broadened due to a restrictedly random distribution of dislocations [1,5]:
The voltage measurement at setting 1 provides the real part of the Fourier coefficient and the measurement at setting 2 provides the imaginary part in Equation 6.
k,v] denotes the kth normalized Fourier coefficient of [P.

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