fourier-series expansion
1Fourier series — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms …
2Fourier series — [foor′ē ər] n. [formulated by FOURIER Baron Jean Baptiste Joseph] Math. the expansion of a periodic function into a series of sines and cosines …
3Relations between Fourier transforms and Fourier series — In the mathematical field of harmonic analysis, the continuous Fourier transform has very precise relations with Fourier series. It is also closely related to the discrete time Fourier transform (DTFT) and the discrete Fourier transform (DFT).… …
4Fourier series — n. Math. an expansion of a periodic function as a series of trigonometric functions …
5Convergence of Fourier series — In mathematics, the question of whether the Fourier series of a periodic function converges to the given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily a given… …
6Half range Fourier series — A half range Fourier series is a Fourier series defined on an interval [0,L] instead of the more common [ L,L] , with the implication that the analyzed function f(x), xin [0,L] should be extended to [ L,0) as either an even or odd function. This… …
7Fourier analysis — In mathematics, Fourier analysis is a subject area which grew out of the study of Fourier series. The subject began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions. The… …
8Fourier optics — is the study of classical optics using techniques involving Fourier transforms and can be seen as an extension of the Huygens Fresnel principle. The underlying theorem that light waves can be described as made up of sinusoidal waves, in a manner… …
9Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …
10Fourier–Bessel series — In mathematics, Fourier–Bessel series are a particular kind of infinite series expansion on a finite interval, based on Bessel functions and as such are part of a large class of expansions based on orthogonal functions. Fourier Bessel series are… …
