Cardinal series to filter oversampled truncated magnetic resonance 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.