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{{r|Fourier transform}}

{{r|Fast Fourier Transform}}

{{r|Fast Fourier transform}}

// The "miminal" Fast Fourier Transform by Dmitrii Kouznetsov

==Fourier transform==

...s C++ routine required for compilation of examples with [[DCTI]], Discrete Fourier transform of the First kind.

{{r|Fourier transform}}

...rom a third vector field, the [[vector potential]] '''A'''. Below, the [[Fourier transform]] of the three real fields '''E''', '''B''', and '''A''' will be introduced

The [[Fourier transform]] translates convolution into [[pointwise operation|pointwise multiplicatio

...trogen-Containing Aromatic Compounds from a Single Electrospray Ionization Fourier Transform Ion Cyclotron Resonance Mass Spectrum of Heavy Petroleum Crude Oil; Kuangna ...biodegraded reservoir and surface crude oils by negative ion electrospray Fourier transform ion cyclotron resonance mass spectrometry;Christine A. Hugheya, Samantha A.

...Gaussian exponential]] exp(−''x''²/2) is a fixed point of the [[Fourier transform]] operator <math>\mathcal{F}</math> defined by ...e value at ''p'' of the Fourier transform <math>\mathcal{F}[f]</math>; the Fourier transform is the result of applying the operator <math>\mathcal{F}</math> to the func

...ll an associated eigenfunction expansion (similar to Fourier series versus Fourier transform). This is important in [[quantum mechanics]], since the one-dimensional [[S

By taking the [[Fourier transform]] of this equation in the time variable, or equivalently, by looking for ti

The decomposition is formulated in '''r'''-space. By a [[Fourier transform]] the decomposition may be formulated in '''k'''-space. This is advantageou

...and using the ordinary rules of integral calculus. The delta function as a Fourier transform of the unit function ''f''(''x'') = 1 (the second property) will be proved The Dirac delta function is the Fourier transform of the unit function ''f''(''x'') = 1.

...dded. Many different transforms can be used; among the commonest are the [[Fourier transform]] for sound data and [[discrete cosine transform]] for images or video. The

...cal calculus tools, such as [[convolution (mathematics)|convolution]] or [[Fourier transform]], can be defined for distributions and, more importantly, the theory of [[

...res]] and [[operating systems|platforms]], and is dedicated to computing [[fourier transform|Fourier Transforms]] on data received from [[radio telescope|radio telescop

...rm multi-chromatic wave would be apt, but is never used). By means of [[Fourier transform|Fourier analysis]] a non-monochromatic wave can be decomposed into its mono

===Fourier transform NMR spectroscopy=== ...is often referred to as the free induction decay, abbreviated as fid). A [[fourier transform]] of the response gives information regarding the frequency response.