The mathematical transform which shifts the phase of all components of some function by is called a Hilbert transform; the components of the magnetization vector can therefore be any Hilbert transform pair (the simplest of which is simply
The Hilbert transform is named after David Hilbert, who first introduced the operator in order to solve a special case of the Riemann–Hilbert problem for holomorphic functions.
Because of its computational efficiency and simplicity, the Hilbert transform is nowadays used for the calculation of the 2D spectra.
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