SpringerImages - Calculation of the projection sweep width. The black rectangle outlines a conventional 2D sub-space of the N-dimensional spectrum, which is spanned by default values of the sweep widths SWi and SWj for the nuclei in the indirect ωi and ωj dimensions. For a given projection with projection angle α (orange line) the value SW for the sweep width can be calculated using the conventional approach of Eq. , resulting in the segment from point A1 to point A2. Alternatively, when using the refined approach of Eq. , one obtains the shorter segment from B1 to B2. The dashed and dotted lines indicate the trajectories for all possible values of the projection angle α of the locations of the points A1,2 (Eq. ) and the points B1,2 (Eq. ), respectively

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Fig 8

Calculation of the projection sweep width. The black rectangle outlines a conventional 2D sub-space of the N-dimensional spectrum, which is spanned by default values of the sweep widths SW_i and SW_j for the nuclei in the indirect ω_i and ω_j dimensions. For a given projection with projection angle α (orange line) the value SW for the sweep width can be calculated using the conventional approach of Eq. , resulting in the segment from point A₁ to point A₂. Alternatively, when using the refined approach of Eq. , one obtains the shorter segment from B₁ to B₂. The dashed and dotted lines indicate the trajectories for all possible values of the projection angle α of the locations of the points A_1,2 (Eq. ) and the points B_1,2 (Eq. ), respectively

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For the recording of projection spectra, an appropriate sweep width for a projection with given projection angles, SW , can be calculated from these default values ( SW_i and SW_j in Fig. 8 ) for the different nuclei in the individual indirect dimensions.

A straightforward approach is the “projected rectangle” (Fig. 8 ), which is guided by the consideration that all expected correlation peaks should be contained in the projection spectrum without aliasing, 9 $$ {SW} = \sum\limits_{i}^{N - 1} {{SW}_{i} \cdot p_{i} }.$$ .

A more refined sweep width selection can be obtained by calculating the standard deviation for the distribution of chemical shifts in a given projection (Fig. 8 ).

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