Institut Navier - Université Paris-Est, 2 allée Kepler, 77420 Champs sur Marne, France.
J Magn Reson. 2010 May;204(1):64-75. doi: 10.1016/j.jmr.2010.02.002. Epub 2010 Feb 19.
Digital low pass filters are routinely used to improve the signal-to-noise ratio of NMR signals, e.g. FID or echoes, when pass band widths of the available analogue filters do not correspond to the spectral width of the signals. Applying digital filters will always necessitate an oversampling of the signal to filter. The digital filters with which the commercial spectrometers are nowadays equipped and most of those known to date from literature were designed to be applied to signals in the time domain. Nevertheless, most of them are aimed at optimising the filtering of signals in the frequency domain and tend to distort them in the time domain, especially when applied to truncated signals. Herein we propose a low pass filter that preserves all the features of the signal in both domains. The method consists in fitting raw NMR data with a finite sum of truncated cardinal sine functions and requires nothing but the signal being a band-limited function. We devised sensible and, in practice, hardly restrictive rules for setting parameters of the filter and applied it to various computer-simulated and experimentally measured truncated data sets to demonstrate its success in filtering both FID and echo signals.
数字低通滤波器通常用于提高 NMR 信号（例如 FID 或回波）的信噪比，当可用模拟滤波器的通带宽度与信号的频谱宽度不对应时。应用数字滤波器总是需要对信号进行过采样以进行滤波。如今，商业光谱仪配备的数字滤波器以及迄今为止大多数文献中已知的数字滤波器都是为应用于时域中的信号而设计的。然而，它们中的大多数旨在优化信号在频域中的滤波，并倾向于在时域中对其进行失真，尤其是在应用于截断信号时。在此，我们提出了一种在两个域中都能保留信号所有特征的低通滤波器。该方法包括用有限项截断的基数正弦函数拟合原始 NMR 数据，并且只需要信号是一个带限函数。我们设计了合理的、实际上几乎没有限制的滤波器参数设置规则，并将其应用于各种计算机模拟和实验测量的截断数据集，以证明其在过滤 FID 和回波信号方面的成功。
