Abstract
The Fourier transform is one of the main tools of analysis with a large number of important applications in physics, technology and statistics. In numerical applications it has to appear in discrete form as the finite Fourier transform. This transform is associated with the theory of characters of finite modules (abelian groups) which forms the first part of this chapter. The remaining parts are devoted to applications, first a proof of the quadratic reciprocity theorem and then numerical applications, in particular the method of computing the finite Fourier transform which is called the fast Fourier transform, FFT.KeywordsFourier TransformCommutative GroupFast Fourier TransformCyclic ModuleBinary DigitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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