Saving Measurement Time in ¹³C NMR Spectroscopy

Abstract

An algorithm to produce acceptably accurate Fourier transform NMR spectra using many fewer transients than commonly obtained is introduced and applied to 13C chemical shift and one-dimensional INADEQUATE Lorentzian type spectra. The algorithm supplies criteria to recognize when to stop transient collection at a time too early for an acceptable spectrum to be produced by Fourier signal processing but not by harmonic inversion signal processing.

A numerical study of the asymptotic convergence characteristics of partial averaged and reweighted Fourier path integral methods

“…(11)] analytically, we consider in this section a robust HI method [20,21], which allows us to fit an arbitrary potential function V(x) to a linear superposition of Gaussian functions…”

“…Singer showed that the usual LennardJones interaction can be fit to good approximation by the sum of two Gaussians. Using the harmonic inversion (HI) method [20,21], we fit the usual Lennard-Jones potential to the sum of two Gaussians. Below we show that the resulting deviations in the properties between the Lennard-Jones and resulting Gaussian fit systems are within acceptable limits.…”

A new signal processing method to observe weak 31P and 17O NMR peaks

“…In reference [1] (where the mathematics supporting this section is given), a signal processing scheme aimed at increasing the sensitivity of signal detection was introduced. Here, it is used to process weak 31 P and 17 O signals.…”

“…Using the sample data available in the FID, a Hermitian correlation matrix is created [1]. The all-positive eigenvalues of this matrix are called the singular values.…”

“…Recently, a new harmonic inversion (HI) signal processing method [1] was proposed for weak NMR signals at or below the threshold of detecting conventional FFT approaches. In this paper, we explore applications of the method to several model problems in NMR detection.…”