Department of Chemistry, University of California, Irvine, CA 92697-2025, USA.
J Magn Reson. 2010 Nov;207(1):17-23. doi: 10.1016/j.jmr.2010.07.019. Epub 2010 Aug 7.
The Filter Diagonalization Method (FDM) has been used to process NMR data in liquids and can be advantageous when the spectrum is sparse enough, the lines are sharp and Lorentzian, raw sensitivity is adequate, and the measured time-domain data is short, so that the Fourier Transform spectrum exhibits distorted line shapes. Noise can adversely impact resolution and/or frequency accuracy in FDM spectral estimates. Paradoxically, more complete data can lead to worse FDM spectra if there is appreciable noise. However, by modifying the numerical method, the FDM noise performance improves significantly, without apparently losing any of the existing advantages. The two key modifications are to adjust the FDM basis functions so that matrix elements computed from them have less noise contribution on average, and to regularize each dimension of a multidimensional spectrum independently. The modifications can be recommended for general-purpose use in the case of somewhat noisy, incomplete data.
Filter Diagonalization Method (FDM) 已被用于处理液体中的 NMR 数据，当谱线足够稀疏、线宽较窄且呈洛伦兹线型、原始灵敏度足够高、且所测量的时域数据较短，以致傅里叶变换谱线呈现出扭曲的线形状时，该方法具有优势。噪声会对 FDM 谱估计的分辨率和/或频率精度产生不利影响。矛盾的是，如果存在可观的噪声，更完整的数据可能会导致更差的 FDM 谱。然而，通过修改数值方法，FDM 的噪声性能会显著提高，而不会明显失去现有的任何优势。这两个关键的修改是调整 FDM 的基函数，使得从它们计算得到的矩阵元素的噪声贡献平均更少，以及对多维谱的每个维度进行独立正则化。在存在一定噪声和不完整数据的情况下，这些修改可以推荐用于通用目的。
