Bayesian Estimation of NMR Spectral Parameters Under Low Signal-to-Noise Conditions

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.