SpringerImages - Schematic representation of data sampling and processing for projections of two indirect dimensions x and y. (a) The time domain is sampled along cross-sections through the origin. The green and red dots are sample points for projections along the time dimensions tx and ty, respectively. The black dots are sampling points for two projections at angles α1 and α2, respectively. (b) Signal envelopes se(t) along the time domain cross-sections. The relaxation rate of a given signal depends on its projection angle (see text). (c) After Fourier transformation, the NMR spectrum in the frequency space, I(ω), is obtained. The intensity at the peak maximum depends on the relaxation rate of the signal (see (b)) and on the processing parameters

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Fig 5

Schematic representation of data sampling and processing for projections of two indirect dimensions x and y. (a) The time domain is sampled along cross-sections through the origin. The green and red dots are sample points for projections along the time dimensions t_x and t_y, respectively. The black dots are sampling points for two projections at angles α₁ and α_2, respectively. (b) Signal envelopes s^e(t) along the time domain cross-sections. The relaxation rate of a given signal depends on its projection angle (see text). (c) After Fourier transformation, the NMR spectrum in the frequency space, I(ω), is obtained. The intensity at the peak maximum depends on the relaxation rate of the signal (see (b)) and on the processing parameters

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The N -dimensional time domain, ( t₁ , t₂ , …, t_N ), is thus sampled at discrete points on the hyperplane $$ t \cdot \vec{p}_{1} \left( {\vec{\varphi }} \right) + t_{N} \cdot \vec{p}_{2} $$ (Fig. 5 a), where t is a time parameter along $$ \vec{p}_{1} \left( {\vec{\varphi }} \right) $$ in the ( N −1)-dimensional time domain subspace of the indirect dimensions, and t_N is the time axis for the direct detection.

Since all cross-sections start at the time domain origin (Fig. 5 a), the signal amplitude at the time origin of a given experiment m , $$ s_{m} \left( 0 \right) $$ , is independent of $$ \vec{\varphi } $$ (Fig. 5 b).

The signal envelopes have a strong impact on the signal intensity in the projection spectra (Fig. 5 b, c)..

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