Digital interpolation of stochastic signals

The process of interpolation seems to be of importance in some areas of digital signal processing, as speech processing, modulation systems and others. Several techniques have been proposed in the past, all of them utilizing a low-pass digital filter, and some of them are optimal in terms of the computation minimization for given design specifications. The common characteristic of these filters is that they are fixed, since they have been constructed, regardless of the structure of the signal to be processed. A new point of view is developed in this paper, where an optimum filter is proposed which takes into account the statistical properties of the stochastic input signal and especially its correlation function. Algorithms and closed forms are suggested, depending on the complexity of the interpolation and the application. In addition, computer simulation results are presented to confirm the validity of the theoretical results, and finally, some open problems are briefly discussed.