COMPARISON OF FOURIER AND BAYESIAN-ANALYSIS OF NMR SIGNALS .2. EXAMINATION OF TRUNCATED FREE INDUCTION DECAY NMR DATA

In a recent report [J, J. Kotyk et al., J. Magn. Reson, 98, 483 (1992) ], estimates of NMR frequency and amplitude parameters obtained from B ayesian probability theory were shown to be more precise and more accu rate than those obtained from the discrete Fourier transform (DFT). Th is previous study examined the effects of varying signal-to-noise rati o and did not address the performance of either probability theory or the DFT as a function of acquisition time, i.e., truncation, Herein, a quantitative comparison between probability theory and the DFT is pre sented and discussed in terms of the accuracy and precision they provi de in estimating the frequency and amplitude from truncated free induc tion decay data, For simplicity, data containing only a single frequen cy are examined. For frequency estimation, Bayesian probability theory gives either more precise and accurate estimates or exactly the same estimates as the DFT. This latter result only occurs when the theory i ndicates that the Bayesian procedure is functionally identical to the DFT, For amplitude estimation, the results presented herein are consis tent with those cited in previous work, Even for the best DFT procedur e, probability theory outperforms the DFT by a factor of two or more d epending on the signal-to-noise ratio and the prior information suppli ed in the analysis. The amplitude estimates from probability theory ar e more precise and/or more accurate than the DFT results for all level s of truncation, Additionally, the only time the DFT amplitude estimat es are more precise (less uncertain) are when they are inaccurate (giv e an incorrect answer). Thus, the use of probability theory offers sig nificant improvement over the use of DFT in highly truncated NMR free induction decay data. (C) 1995 Academic Press, Inc.