Cardinal Series Filter for NMR Signals
Abstract
We designed a digital low pass filter suitable for processing truncated NMR signals. In developing our algorithm we were inspired by the Bayesian approach to solving inverse problems. Our method consists in fitting raw NMR data with a finite series of truncated cardinal sine functions and requires nothing but the signal being band-limited. 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 data sets to demonstrate its filtering performance and tolerance towards signal truncations. We believe that our method can be particularly useful for processing data collected in numerous NMR experiments in which relevant information is extracted direct from the signal in the time domain.