PlanetPhysics/Table of Fourier and Generalized Transforms

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Table of Fourier and generalized Fourier transforms
Fourier transforms are being very widely employed in physical, chemical and engineering applications for harmonic analysis, as well as for: processing acquired data such as spectroscopic, image processing (as for example in Astrophysics, elctron microscopy, optics), structure determination (e.g., X-ray, neutron, electron diffraction), chemical Hyperspectral Imaging (FT-NIR, FT-IR), and so on. Theoretical studies in quantum mechanics (QM ), QCD, QG, AQFT, quantum theories on a lattice (QTL ) also employ Fourier transforms.

Fourier-Stieltjes transforms and measured groupoid transforms are useful generalizations of the (much simpler) Fourier transform, as concisely shown in the following table.

\subsubsection*{Fourier Transforms and Generalized FTs}