Interpolation of the natural responses of physical systems with rational transfer functions
L.P. Bolgiano · Numerical Functional Analysis and Optimization · 1980
The infinite Gregory-Newton series is shown capable of interpolating unbandlimited signals which have the form of the natural responses of linear systems. Like the Whittaker cardinal function interpolation, this interpolation requires the sampling rate to satisfy a certain criterion. This criterion differs from the Nyquist criterion in that the signals are characterized by pole frequencies, instead of maximum frequencies, which must be less than a submultiple of the sampling rate.