Adaptive restoration of unknown samples in certain time-discrete signals

Algorithms for the restoration of unknown samples at known positions embedded in a neighborhood of known samples are discussed. First, this restoration problem is treated as a (nonadaptive) linear minimum variance estimation problem. It is shown that the optimal linear minimum variance interpolator for unknown samples from an autoregressive process uses only a finite neighborhood of known samples, whereas in general this neighborhood is infinite. Second, for signals that can be modeled as autoregressive processes, an adaptive solution to the restoration problem is given.