Many digital systems have need for continuous-type output for oscilloscope display, process control, or hybrid computation. This paper presents a generalization and unification of the theory of extrapolation and reconstruction of sampled data. This generalization allows implementation of a recursive algorithm or digital filter in conjunction with the continuous data reconstruction. The general procedure is demonstrated for the implementation of an nth-order recursion relation using polynomial or exponential data reconstruction requiring only a single resetting integrator for the general nth-order reconstructor.