Non-Uniform Sampling in NMR Spectroscopy and the Preservation of Spectral Knowledge in the Time and Frequency Domains

Abstract

The increased sensitivity under weighted non-uniform sampling (NUS) is demonstrated and quantified using Monte Carlo simulations of nuclear magnetic resonance (NMR) time- and frequency-domain signals. The concept of spectral knowledge is introduced and shown to be superior to the frequency-domain signal-to-noise ratio for assessing the quality of NMR data. Two methods for rigorously preserving spectral knowledge and the time-domain NUS knowledge enhancement upon transformation to the frequency domain are demonstrated, both theoretically and numerically. The first, non-uniform weighted sampling using consistent root-mean-square noise, is applicable to data sampled on the Nyquist grid, whereas the second, the block Fourier transform using consistent root-mean-square noise, can be used to transform time-domain data acquired with arbitrary, off-grid NUS.

Non-uniform sampling in pulse dipolar spectroscopy by EPR: the redistribution of noise and the optimization of data acquisition

“…On the other hand, with regularization methods lacking linearity, the noise in the distance spectrum depends not only on s(T), but also on P(r). 17 The linearity of MeTA provides a simple, convenient tool to study how random noise propagates into the distance spectrum regardless of the distance distribution function. Without that linearity, every P(r) can be a special case, requiring its own individual set of calculations.…”

“…NUS is actively used in NMR with several reviews, 17,[30][31][32][33][34] and NUA has been tried. 35,36 Compressed sensing can be considered a form of NUS, 37,38 and is used in many forms of spectroscopy and imaging, including NMR, but uses a rather different approach to convert raw data into a spectrum than we are considering here.…”

“…But the regularization is almost always based on f (r), which means the errors, i.e., noise, that propagate into the resulting distance spectrum depends on P(r). 17 The noise and the distance distribution function become quite entangled. This regularization approach makes it difficult to understand how random noise affects experimental results because identical noise in the dipolar trace affects the distance spectrum differently for every different P(r).…”

A Monte Carlo Method for Analyzing Systematic and Random Uncertainty in Quantitative Nuclear Magnetic Resonance Measurements

“…Indeed, previous theoretical and computational work has shed light on various aspects of how noise acquired and processed using different schemes may impact single signal quantification in NMR. − Under favorable experimental conditions (i.e., well-shimmed, thermally stable system), these may include the choice of spectroscopic parameters, such as the spectral width (SW), number of time domain points sampled, and total acquisition time; processing parameters, such as apodization and zero-filling (ZF); and the signal-to-noise ratios (SNRs) and linewidths of the signals being measured. However, a general approach detailing the impact of these factors on arbitrary qNMR ratio measurements does not currently exist to the best of the author’s knowledge.…”

Window Function for Chirped Pulse Spectroscopy with Enhanced Signal-to-noise Ratio and Lineshape Correction

“…Combined with window functions, more sophisticated methods based on non-uniform [6] sampling have been applied, mostly in multi-dimensional NMR, to further increase the SnR without losing spectral resolution. [7,8] The invention of chirped pulse Fourier-transform (CP-FT) microwave spectroscopy [3] allowed extremely rapid and broadband up to several tens of GHz acquisition of a rotational spectrum. Due to this double advantage, CP-FT spectroscopy has become actively used for structural determinations in large and complex molecular systems (large molecules and clusters) [9,10], for reaction dynamics and kinetics studies [11][12][13], and for rapid chemical composition analysis [14,15].…”