Department of Chemistry, University of California, Irvine, CA 92697-2025, USA.
J Magn Reson. 2012 Jan;214(1):15-21. doi: 10.1016/j.jmr.2011.09.044. Epub 2011 Sep 29.
A more robust way to obtain a high-resolution multidimensional NMR spectrum from limited data sets is described. The Filter Diagonalization Method (FDM) is used to analyze phase-modulated data and cast the spectrum in terms of phase-sensitive Lorentzian "phase-twist" peaks. These spectra are then used to obtain absorption-mode phase-sensitive spectra. In contrast to earlier implementations of multidimensional FDM, the absolute phase of the data need not be known beforehand, and linear phase corrections in each frequency dimension are possible, if they are required. Regularization is employed to improve the conditioning of the linear algebra problems that must be solved to obtain the spectral estimate. While regularization smoothes away noise and small peaks, a hybrid method allows the true noise floor to be correctly represented in the final result. Line shape transformation to a Gaussian-like shape improves the clarity of the spectra, and is achieved by a conventional Lorentzian-to-Gaussian transformation in the time-domain, after inverse Fourier transformation of the FDM spectra. The results obtained highlight the danger of not using proper phase-sensitive line shapes in the spectral estimate. The advantages of the new method for the spectral estimate are the following: (i) the spectrum can be phased by conventional means after it is obtained; (ii) there is a true and accurate noise floor; and (iii) there is some indication of the quality of fit in each local region of the spectrum. The method is illustrated with 2D NMR data for the first time, but is applicable to n-dimensional data without any restriction on the number of time/frequency dimensions.
一种从有限数据集获得高分辨率多维 NMR 谱的更稳健方法被描述。滤波器对角化方法（FDM）用于分析相位调制数据，并根据相敏洛伦兹“相位扭曲”峰来构建谱。然后，这些谱用于获得吸收模式相敏谱。与早期的多维 FDM 实现相比，不需要事先知道数据的绝对相位，并且如果需要，可以在每个频率维度中进行线性相位校正。正则化用于改善必须解决的线性代数问题的条件，以获得谱估计。虽然正则化可以平滑噪声和小峰，但混合方法允许在最终结果中正确表示真实的噪声底。通过在频域中进行常规的洛伦兹到高斯变换，然后对 FDM 谱进行傅里叶逆变换，将线形状变换为类似高斯的形状，从而改善谱的清晰度。所得到的结果强调了在谱估计中不使用适当的相敏线形状的危险。新方法在谱估计方面的优点如下：（i）可以在获得谱之后通过常规手段对其进行相位处理；（ii）存在真实准确的噪声底；（iii）在谱的每个局部区域都有一些拟合质量的指示。该方法首次用 2D NMR 数据进行了说明，但适用于 n 维数据，对时间/频率维度的数量没有任何限制。
