Sometimes the components are known first, and the unknown function is synthesized īy a Fourier series. The components of a particular function are determined by analysis techniques described in this article. The number of components is theoretically infinite, in which case the other parameters can be chosen to cause the series to converge to almost any well behaved periodic function (see Pathological and Dirichlet–Jordan test). With appropriate choices, one cycle (or period) of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or period), the number of components, and their amplitudes and phase parameters. A Fourier series ( / ˈ f ʊr i eɪ, - i ər/ ) is a summation of harmonically related sinusoidal functions, also known as components or harmonics.
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