Abstract
The Bayesian statistical method of spectral estimation is applied to NMR free induction decay signals at various values of signal-to-noise ratio (SNR). The frequency and amplitude estimates from the Bayesian calculations are more accurate than those from the commonly used fast Fourier transformation (FFT) of the same data sets. Both real and synthetic data sets are examined with the Bayesian results being superior in all cases. In addition to the superior performance at low SNR the Bayesian derived amplitudes and frequency estimates were not as affected by signal decay as in Fourier Transformed spectra. Finally, the amplitudes obtained are equal to the FFT integrated intensities resulting in an apparent frequency domain signal-to-noise ratio (SNR) greater than the FFT SNR by a factor proportional to the FFT frequency domain linewidth. For typical high resolution spectra this improvement was approximately a factor of 2.5. Even greater improvement is obtained when rapidly decaying signals are analyzed. Bayesian computation time for the 6 line p-chloroanaline and chloroform spectrum was approximately 12 minutes on a modern computer work station.
| Original language | English |
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| Pages (from-to) | 1559-1570 |
| Number of pages | 12 |
| Journal | Spectroscopy Letters |
| Volume | 26 |
| Issue number | 8 |
| DOIs | |
| State | Published - Sep 1 1993 |
Funding
observed in the FT spectrum are obtained with modest computation time. In future implementations it should be possible to extract and characterize signals that are not observable at all in the FT spectrum at an increased cost of computation time or to resolve closely spaced lines that are not resolved by FT analysis without degradation of the SNR. The studies reported here involved simulations or data acquisition under conditions typically utilized in Fourier transform NMR specuoscopy. Because of differing requirements of the Bayesian method, alternative data acquisition schemes may be employed that will provide even greater improvement over the FT spectrum For example, since no artifacts such as sinc wiggles are introduced, one need not continue an acquisition until the signal completely decays away allowing the use of smaller data sets. A future paper will examine the data acquisition ramifications of Bayesian spectral estimation. The superior frequency and amplitude estimating ability suggest futun applications to situations in which rapid signal decay introduces excessive line broadening in the spectrum or where the greater computational time is offset by decreased acquisition time of low SNR samples. Some examples of potential applications include specm of quadrupolar relaxed nuclei such as I4N, "0 and 33S where linewidths are a serious problem and studies of chemical systems undergoing chemical exchange at intermediate rates where extreme broadening can also occurz5 The ability to determine amplitudes from noisy signals suggests applications involving quantitative measurements of dilute components where the excessive acquisition time required for FT analysis compensates for the increased Bayesian computation time. Examples of applications to each of these problem areas will be reported in the near future. Acknowledgements: Support of this work in part by NSF EPSCoR Grant EHR 9108765 is gratefully acknowledged. LEQSF grant (1990-91)-ENH-53 for purchase of the NMR spectrometer is also gratefully acknowledged. Presented in part at Pittcon'92, New Orleans, La., March, 1992.
| Funder number |
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| EHR 9108765 |
Keywords
- Bayesian Estimation
- Low Signal-to-Noise Ratio
- NMR