Beyond Fourier

Abstract

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.

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

“…3 ) max 2 (25) and displayed in Figure 5. The NUS knowledge enhancement is a quantitative measure of the advantage to NUS acquisition relative to standard US.…”

“…Experimental techniques for polarization transfer, including hyperpolarization from dynamic nuclear polarization (DNP), , parahydrogen, and photo-chemically induced DNP, and hardware developments such as higher magnetic fields and cryoprobes are just a few examples of the many approaches taken to accomplish this. The technique of weighted non-uniform sampling (NUS) in the indirect dimensions has also been proposed to increase sensitivity − as well as shorten the acquisition of multidimensional spectra. − NUS refers to any pattern of collecting samples that is done at irregular time intervals or with variable numbers of transients taken at different time points. − To achieve higher sensitivity with a finite number of measured points, weighted NUS places more samples at earlier times in the free-induction decay (FID) when the signal is stronger. − The predicted gains in sensitivity under weighted NUS (1.2–2) , are not as large as those for some of the techniques mentioned above but can be incorporated into any multidimensional experiment and compound with the number of indirect dimensions …”

XLSY: Extra‐Large NMR Spectroscopy

“…[1] However,t he task of reconstructing and handling of very large spectra is still awaiting ag ood solution. [1] However,t he task of reconstructing and handling of very large spectra is still awaiting ag ood solution.…”