High resolution NMR spectroscopy using a recursive algorithm.

When the DFT (discrete Fourier transform) is used as a method for obtaining NMR (nuclear magnetic resonance) spectrum, resolution of the obtained NMR spectrum depends clearly on spin-spin relaxation times of the nucleus and the sampled number of NMR signal. That is, the NMR spectrum is affected by decay of NMR signal due to the relaxation times and errors associated with discrete approximation of NMR spectrum. As a results, its resolution is degraded and the spectrum disagrees with the density distribution of the nucleus. In the present paper, we propose a new NMR spectrum estimation method for reducing their effects, demonstrating a high resolution NMR spectrum which is closer to the density distribution than that of the DFT. The proposed method is derived from applying the Kalman filter or the recursive least-square method to a NMR signal model based on Bloch equation. Under various conditions, the proposed method is compared with the DFT using a proton 1H NMR signal observed from mayonnaise in a 2 [T] static magnetic field. The results show that if spin-spin relaxation times are known previously, the proposed method can provide a higher resolution NMR spectrum than the DFT. In addition, it is shown that the method can reduce the discrete approximation errors of NMR spectrum. Finally, we demonstrate that if frequency components of sources of NMR signal are present in a limited range in frequency domain of interest, the method can magnify NMR spectrum with a sampling time and interval fixed.