![]() Weighted sampling is very easy to implement experimentally and improves the sensitivity without compromising the quality of the resulting spectra, even for cases of poor quantization, if for example the first half of the points in the indirect dimension(s) are recorded with double the number of transients compared to the second half. the number of discrete steps used experimentally to approximate the window function. Furthermore we examine the dependence of the sensitivity gain on the chosen quantization, e.g. If we choose the acquisition weights to follow the apodization function used to process the equivalent conventional data, the achievable sensitivity gain by weighted sampling is determined by the equivalent noise bandwidth of the apodization function, a property that is tabulated in books or reviews of window functions (e.g. In this contribution we derive a general expression for the sensitivity of a weighted acquisition experiment. 1991) or for a smooth approximations of selected apodization functions (Waudby and Christodoulou 2012). A second reason could be a missing theoretical derivation of the achievable sensitivity gain, which was previously addressed qualitatively (Kumar et al. 1991) and 256 (Waudby and Christodoulou 2012), respectively) which might suggest that the method is limited to selected 2D applications, but practically prohibitive for 3D or 4D spectra. One reason for this might be that fact that in both above references the number of measured transients per time increment is quite large in the example spectra (40 (Kumar et al. 1991 Waudby and Christodoulou 2012), but we could not find applications of this method for recording 3D spectra in standard protein or RNA NMR studies. The alternative of acquiring all points on the grid with different number of transients per point has been discussed in the literature (Kumar et al. Common to all of these publications is the implementation of the sampling schedule as a sequence of sampled data points with a uniform number of transient recorded per point interleaved with gaps. Optimal sampling schedules for such experiments and their comparison in terms of sensitivity are discussed controversially (Zambrello et al. NUS applications in this so-called sensitivity limited regime are usually implemented by choosing the sampling probability of a point on a sparse uniform grid based on the signal envelope function (Hyberts et al. Many of the standard 3D experiments are recorded with a larger number of transients per time domain point than required for signal selection. In biomolecular experiments low sensitivity is a major obstacle. 2012 Orekhov and Jaravine 2011) have been proposed. 2018) and processing schemes (Chylla and Markley 1993, 1995 Gutmanas et al. 2011 Kazimierczuk and Orekhov 2011 Craft et al. For these so-called nonuniform sampling (NUS) methods a number of different sampling schedules (Barna et al. For the second method the conventional digital Fourier transformation (DFT) leads to very low quality spectra and thus alternative non-linear processing methods are required to reconstruct the spectrum. The first method leads to an effective reduction of the dimensionality by projecting the coupled time domains onto one plane (Freeman and Kupce 2012 Hiller and Wider 2012). 1993) or by recording only a random fraction of the sampling points (Barna et al. 1994 Kim and Szyperski 2003 Szyperski et al. This limitation can be overcome by altering the uniform sampling scheme of the indirect dimension(s), either by coupling the increments of two or more indirect dimensions (Brutscher et al. In practice, this leads either to long experimental times or compromises in spectral resolution and/or sensitivity. The sampling rate of an indirect frequency dimension of these spectra is related to the spectral range to be covered through the Nyquist relation and spectral resolution requirements dictate the total data length of the data recording. The NMR characterization of biomolecules generally requires the acquisition of a number of multidimensional spectra. Biomolecules are especially challenging in this respect, since they are prone to strong signal overlap, severe line broadening and low sensitivity. Any improvement of one of them without compromising the other is of major importance to allow efficient data analysis. Resolution and sensitivity are the essential quality parameters of high field NMR spectra.
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