On the reconstruction of a smooth function out of its samples

The reconstruction of smooth signals out of its samples will be considered. Using a sampling frequency higher than the Nyquist rate we are able to define a family of appropriate idealized systems for the reconstruction. They are approximated by a realizable system consisting of a digital filter followed by a D/A-converter and an analog smoothing filter. The design of the digital (nonrecursive) filter will be performed in the frequency and time domain. Some examples will demonstrate these reconstruction procedures.