Fourier analysis

Uncommon card · No. 145910

In mathematics, the sciences, and engineering, Fourier analysis () is the study of the way general functions on the real line, circle, integers, finite cyclic group or general locally compact Abelian group may be represented or approximated by sums of trigonometric functions or more conveniently, complex exponentials. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Fourier analysis has applications in many areas of pure and applied mathematics, in the sciences and in engineering. The process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note...

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