Lineshapes and artifacts in Multidimensional Fourier Transform of arbitrary sampled NMR data sets

Narrow peaks and high dimensionalities: Exploiting the advantages of random sampling

“…However, this is not the case of off-grid random sampling processed by MFT. In our recent works [23,24] we have shown that artifacts from random sampling appear even when sampling density is above Nyquist condition. Moreover, they do not origin from integration imperfections, but rather from breaking of conventional Sampling Theorem, which stands that function with finite spectrum may be fully specified by its values only if they are at least at Nyquist density, like in interlaced sampling schemes [27].…”

“…PDF for variable t i can be chosen arbitrary, depending on the shape of signal (decaying or not) and affects line shape in the same way as weighting function [24]. Thus, for simplicity, uniform PDF will be considered for generation of sampling points.…”

“…We have proposed the off-grid random sampling, which is in our opinion the best option for non-linear sampling, i.e. produces Point Spread Function (PSF) of the best signal-to-artifact ratio [23,24]. The time domain signal is sampled evenly and each point differs from the others in values of all its coordinates (or, in perfect case, there is infinitesimally small probability that it will not differ).…”

Optimization of random time domain sampling in multidimensional NMR

“…Recently, we have shown that off-grid random sampling is the best choice because of the lowest artifact level-artifacts appear in each spectral region, but they are very well spread over the frequency domain [8,14]. We have also revealed that even slight modifications of random sampling could substantially improve results [14].…”

Random phase detection in multidimensional NMR

“…The approach is not without limitations: Nonuniform sampling (NUS) introduces sampling artifacts that present severe limitations. When the discrete Fourier transform (DFT) is used to obtain a frequency spectrum from NUS data (16)(17)(18), the resulting spectrum is the convolution of the sampling schedules's point-spread function (PSF) with the true spectrum (19). A host of non-Fourier methods of spectrum analysis can effectively deconvolve the PSF from the NUS spectrum (3,8,15,16,(20)(21)(22)(23)(24)(25)(26)(27)(28), and although successful to a degree, their ability to remove sampling artifacts is invariably limited by the presence of noise.…”