Reference deconvolution, phase correction, and line listing of NMR spectra by the 1D filter diagonalization method.

We describe a new way to attack the problem of identifying and quantifying the number of NMR transitions in a given NMR spectrum. The goal is to reduce the spectrum to a tabular line list of peak positions, widths, amplitudes, and phases, and to have this line list be of high fidelity. In this context "high fidelity" means that each true NMR transition is represented by a single entry, with no spurious entries and no missed peaks. A high fidelity line list allows the measurement of chemical shifts and coupling constants with good accuracy and precision and is the ultimate in data compression. There are two parts to the problem. The first is to overcome common imperfections: the non-Lorentzian lineshapes that can arise whenever the magnetic field inhomogeneity is less than perfect, and nonzero time delays that cause frequency-dependent phase errors. The second is to fit the spectral features to a model of Lorentzian lines. We use the recently developed filter diagonalization method (FDM) to accomplish the reference deconvolution, the phase correction, and the fitting, and show good progress toward the goal of obtaining a high fidelity line list.