Lorentz-Gaussian transformation

Figure 3.37. The Lorentz-Gauss transformation ( Gaussian multiplication ) can be used to improve resolution, (a) Raw FID and spectrum following Fourier transformation and results after the L-G transformation with (b) lb = -IHz, gb = 0.2 and (c) lb =...

Abstract Hilbert space, 426 Accuracy of computed root, 78 Acharga, R., 498,539,560 Additive Gaussian noise channel, 242 Adjoint spinor transformation under Lorentz transformation, 533 Admissible wave function, 552 Aitkin s method, 79 Akhiezer, A., 723 Algebra, Clifford, 520 Algebraic problem, 52 linear, 53... 

If we can set Rre to cancel exactly the original decay of the FID then the result of this process is to generate a time-domain function which only has a Gaussian decay. The resulting peak in the spectrum will have a Gaussian lineshape, which is often considered to be superior to the Lorentzian as it is narrower at the base the two lineshapes are compared in Fig. 4.12. This transformation to a Gaussian lineshape is often called the Lorentz-to-Gauss transformation. 

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