The Ghost Sampling Sequence Method

An interpolation formula involves samples of the observed phenomenon and functions depending on the sampling times. For instance, the classic Shannon formula is based on the observations at periodic times and the values of the cardinal series at these times. But, in real computations, only a finite number of these observations are taken into account, in a limited time window. Because what is measured outside the window does not intervene, it is often possible to use a sampling time sequence made of the real times inside the window, and completed by an arbitrary time sequence taken outside the window. The latter is a “ghost sequence” because the values of the object to reconstruct at these times are not known and are not used in real computations.