Digital Filtering, Nyquist Fold-Backs and Signal-to-Noise Ratio

Modern NMR spectrometers use digital filtering to improve the quality of the data. Digital filtering is achieved in three steps:

1. Despite the spectral width requested by the user, the spectrometer oversamples the FID as if a very large spectral width was requested (i.e. short dwell time).

2. Depending on the requested spectral width, a digital filter is calculated and applied to the oversampled FID by the spectrometer.

3. The digitally filtered oversampled data is decimated according to the originally requested spectral width and then Fourier transformed to produce an NMR spectrum.

These steps are schematically illustrated in the figure below.Note that digital filtering applied as in the figure, will suppress Nyquist fold-back signals but more importantly, it will suppress noise from outside the requested spectral width from folding into the spectrum. This suppression of folded in noise represents a significant improvement in the signal-to-noise ratio compared to a spectrum acquired without the use of digital filters..