Superresolution of FT-NMR Spectra by the Maximum Entropy Method and AR Model Fitting with Singular Value Decomposition

The complex maximum entropy method and complex autoregressive model fitting with the singular value decomposition method (SVD) were applied to the free induction decay signal data obtained with a Fourier transform nuclear magnetic resonance spectrometer to estimate superresolved NMR spectra. The practical estimation of superresolved NMR spectra are shown on the data of phosphorus-31 nuclear magnetic resonance spectra. These methods provide sharp peaks and high signal-to-noise ratio compared with conventional fast Fourier transform. The SVD method was more suitable for estimating superresolved NMR spectra than the MEM because the SVD method allowed high-order estimation without spurious peaks, and it was easy to determine the order and the rank.