Cardinal series to restore NMR-signals dominated by strong inhomogeneous broadening

[Display omitted] ► Method for interpolation of missing temporal signal. ► Method for extrapolation of the intensity of the missing initial part of FIDs. ► Robust signal reconstruction from non-uniform samples by means of cardinal series. ► Method for keeping control of the spectral band during Lagrange interpolation. We have devised two numerical methods of restoring incomplete band-limited NMR-signals to integrity by either interpolating or extrapolating them. Both methods are based on use of the finite cardinal series, whose filtering properties were discussed previously, to model signals. They require no prior knowledge about the system under study, but only that the available parts of the signal were oversampled enough. The methods were tested on two types of computer-simulated signal. It proved superior to the linear prediction methods and Lagrange interpolation when applied to signals measured in highly inhomogeneous magnetic fields. The extrapolation method was then applied to restore experimentally-measured refocused FID-signals of a porous medium. The missing parts of the signal of up to several times the size of its Nyquist period could be recovered by either method.