fourier series

English - Turkish

Definition of fourier series in English Turkish dictionary

fourıer serisi

fourier serisi

(Askeri) fourier serileri

(Bilgisayar,Matematik) Fourier dizisi

Related Terms

discrete fourier series

(Bilgisayar,Teknik) ayrık fourier dizisi

discrete Fourier series

ayrik Fourier dizisi

English - English

Definition of fourier series in English English dictionary

A series of cosine and sine functions or complex exponentials resulting from the decomposition of a periodic function

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. In mathematics, an infinite series used to solve special types of differential equations. It consists of an infinite sum of sines and cosines, and because it is periodic (i.e., its values repeat over fixed intervals), it is a useful tool in analyzing periodic functions. Though investigated by Leonhard Euler, among others, the idea was named for Joseph Fourier, who fully explored its consequences, including important applications in engineering, particularly in heat conduction

A series proposed by the French mathematician Fourier about the year 1807 The series involves the sines and cosines of whole multiples of a varying angle and is usually written in the following form: y = Ho + A1 sin x + A2 sin 2x + A3 sin 3x + B1 cos x + B2 cos 2x + B3 cos 3x + By taking a sufficient number of terms the series may be made to represent any periodic function of x

The mathematical basis of harmonic analysis of tides and of tidal predictions, a series of sinusoids of different frequencies representing different tidal harmonic constituents First presented in 1807 by Fourier as a tool for representing any periodic function

An infinite series of the form Such series represent singly periodic meromorphic functions f(z), where f(z+1) = f(z) for all z There is an extensive theory developed around the properties of such series, having many uses in both theoretical and applied mathematics

The representation of a function f(x) in an interval (-L, L) by a series consisting of sines and cosines with a common period 2L, in the form, where the Fourier coefficients are defined as and

A method that defines a periodic or discontinuous function as a series of sine and cosine waves, and can be used to predict a value or the level of system response

the sum of a series of trigonometric expressions; used in the analysis of periodic functions

Hyphenation

Fou·rier se·ries

Etymology

() Named after Joseph Fourier, a French mathematician