In NMR, this step would be equivalent to taking a large sweep width spectrum and setting to zero intensity those spectral frequencies which are farther than some distance from the center of the spectrum. Digital filtering is the removal of these frequencies using the time domain signal. To filter out frequencies above f o from the time domain signal, the signal must be convolved with the Fourier transform of the rectangular function, a sinc function. This process eliminates frequencies greater than f o from the time domain signal. Fourier transforming the resultant time domain signal yields a frequency domain signal without the higher frequencies.
Decimation is the elimination of data points from a data set.
Decimating the digitally filtered data above, followed by a Fourier transform, will reduce the data set by a factor of five. High speed digitizers, capable of digitizing at 2 MHz, and dedicated high speed integrated circuits, capable of performing the convolution on the time domain data as it is being recorded, are used to realize this procedure. There are some important safety considerations which one should be familiar with before using an NMR spectrometer. These concern the use of strong magnetic fields and cryogenic liquids. Magnetic fields from high field magnets can literally pick up and pull ferromagnetic items into the bore of the magnet.