Application of a New Method of High-Resolution Spectral Analysis, “Sompi,” for Free Induction Decay of Nuclear Magnetic Resonance

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Abstract
A new spectral analysis method, “Sompi,” proposed for seismogram analysis based on the autoregressive (AR) model is shown to be useful in extracting unbiased NMR spectra with high resolution and high sensitivity from FID data. The Sompi method deconvolutes the given time series data into a set of spectral lines characterized by frequency, decay constant, initial amplitude, and initial phase. In order to determine the number of spectral lines in the AR modeling of FID data, the Akaike information criterion (AIC) is extended to the model with two parameters: an AR order which specifies the number of the candidate spectral lines, and the number of spectral lines with finite power that exist. The use of the Sompi method combined with the two-parameter AIC is shown to give an accurate and reliable spectrum by analyzing the synthetic data with white noise superimposed. The spectral resolution by the Sompi method is shown to be improved further by means of an intentional aliasing of narrow-band filtered data. The present method is demonstrated by analyzing the observed NMR data on Polyvinylchloride to resolve fine structure which cannot be recognized by FFT.