Nonuniform sampling and spectral aliasing

Abstract

The Nyquist theorem stipulates the largest sampling interval sufficient to avoid aliasing is the reciprocal of the spectral bandwidth. When data are not sampled uniformly, the Nyquist theorem no longer applies, and aliasing phenomena become more complex. For samples selected from an evenly spaced grid, signals that are within the nominal bandwidth of the grid can give rise to aliases. The effective bandwidth afforded by a set of nonuniformly sampled evolution times does not necessarily correspond to spacing of the grid from which the samples are selected, but instead depends on the actual distribution of sample times. For conventional uniform sampling there is no distinction between the grid spacing and the sampling interval. For nonuniform sampling, an effective bandwidth can be inferred from the greatest common divisor of the sample times, provided that none of the sample times are irrational. A simple way to increase the effective bandwidth for a set of nonuniformly spaced samples is to randomly select them from an oversampled grid. For a given grid spacing, “bursty” sampling helps to minimize aliasing artifacts. We show that some spectral artifacts arising from nonuniform sampling are aliases, and that increasing the effective bandwidth shifts these artifacts out of the spectral window and improves spectral quality. An advantage of nonuniform sampling is that some of the benefits of oversampling can be realized without incurring experiment time or resolution penalties. We illustrate the improvements that can be obtained with nonuniform sampling in the indirect dimension of a SOFAST-HMQC experiment.

Simultaneous acquisition of three NMR spectra in a single experiment for rapid resonance assignments in metabolomics

“…30,31,35,[40][41][42][43][44][45] This is exemplified in figure 6, which shows the construction of the 13 C multiplicity edited GFT (3,2)D spectrum at 50% of deletion of the points (chosen with Poisson gap sampling 31 ) in the indirect dimension. The spectra with 50% NUS was acquired with half the measurement time as 100%.…”

“…Notwithstanding this fact, only a few attempts have been made to reduce the acquisition time of high-dimensional NMR spectra for metabolomics. 8 The different fast NMR methods and their combinations developed during the past decade for proteins and nucleic acids such as single-scan NMR spectroscopy (ultrafast NMR), [9][10][11][12][13] HADMARD encoding, 14 NMR [15][16][17][18][19] and G-matrix Fourier transform (GFT) NMR, 20-24 parallel receivers, 25,26 covariance NMR, 27,28 non-uniform sampling, 29-31 rapid pulsing (reducing inter scan delay) [32][33][34] and spectral aliasing 35 have not been satisfactorily explored in metabolomics, where their potential will provide the greatest impact.…”

Can We Determine a Protein Structure Quickly?

“…There are indeed promising new ways to break this bottleneck. The new methodologies of non-uniform sampling [62][63] , labeling a domain [64][65] , selective labeling [66][67][68] , and more powerful NMR machines will eventually allow us to deal with larger proteins. Computational problems arising along with these new technologies will be very interesting.…”

Combining methods for speeding up multi-dimensional acquisition. Sparse sampling and fast pulsing methods for unfolded proteins

“…In contrast to single scan experiments [5], fast pulsing methods such as BEST-experiments are fully compatible with non-linear sampling methods. A first combination of these two concepts has been reported by Maciejewski et al [15] while studying aliasing in non-uniform sampling. Here, we will show that well-resolved 3D spectra can be obtained overnight, and 4D experiments in two days by combining fast pulsing and non-uniform sampling.…”