# 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
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]
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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Fourier coefficient peaks with two significant frequencies at k=1 and k = number of days are commons to all 12 months.
Our calibration model (based on 1971-72 and 2008-09 data) was built using two Fourier coefficient pairs for pond temperature and a single Fourier coefficient pair for air temperature, and it produced a strong fit to observed data ([R.sup.2] = 0.81; RSME = 1.6; Fig.
We notice that 2D FFT can be used to obtain the Fourier coefficient matrix [mathematical expression not reproducible] rapidly.
The uncertainty of a Fourier coefficient, relying on the Nyquist assumptions, scales like [[sigma].sub.D]/[f.sub.Ny] (noise level/maximum bandwidth) which follows from the linear uncertainty propagation for (13).
As it has been mentioned earlier, Fourier coefficient of nth harmonic of current waveform of type (1) can be expressed in form (3).
Equation (11) means that, to evaluate the Fourier coefficient at the 2D frequency coordinate [??], we need to evaluate the Fourier transform of the volume at the coordinate [mathematical expression not reproducible] and then multiply by the corresponding phase term, [mathematical expression not reproducible], to account for the shift in the images.
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.
Note that the restrictions on the kernel of integral equation and on the function Y(t) yield the following estimates of the kernel Fourier coefficients, [absolute value of [c.sub.n,m]] < U/[[absolute value of n].sup.j][[absolute value of m].sup.p], and of Y(t) Fourier coefficient [absolute value of [[??].sub.k]] < T/[[absolute value of k].sup.2].
where [[lambda].sub.nk] is the Fourier coefficient of order n x k in the Fourier expansion of the covariance function of X.
We will prove that "morally" [beta] has the same sign as the degree-2 Fourier coefficient of P and that if one of them is 0 then so is the other.
Recalling that [G.sub.j] = [[phi].sub.j] [Zg.sub.j], we use equation (2.1) to compute that the Fourier coefficient [c.sub.N,-M] of Z([psi]Zf) * [ZG.sub.j] is

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