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:
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
References in periodicals archive ?
To simulate a pavement roughness excitation, there are four existing simulated methods for the time-domain model: white noise filtration method, superposition of harmonic (namely, trigonometric series superposition method), AR (autoregression), and AMAR method based on the discrete time sequence and discrete sampling by PSD [21].
Zygmund, Trigonometric Series, Cambridge University Press, London, UK, 1959.
[27] Tikhonov, S., Trigonometric series with general monotone coefficients.
Tikhonov, "Trigonometric series with general monotone coefficients," Journal of Mathematical Analysis and Applications, vol.
When performing function fitting with trigonometric series, use the least squares method to determine the undetermined coefficients; therefore,
One denotes also by A[P.sub.[phi]](R, C) the metric space whose elements are the trigonometric series of the form (1.1), under the main assumptions (1.2), (1.4), and with the distance function defined by (1.6).
Over the years and under different names statistical convergence has been discussed in the theory of Fourier analysis, Ergodic theory, Number theory, Measure theory, Trigonometric series, Turnpike theory and Banach spaces.
An Accelerated Trigonometric Series Representation for the Displacement Function.
Zygmund, Trigonometric Series, I, II, Cambridge University Press, 2nd edition, 1968.
The following trigonometric series expressions for the logarithmic derivative with respect to z of Jacobi Theta functions will be very useful in this paper,