Adaptive restoration of unknown samples in certain time-discrete signals

In this paper algorithms for the restoration of unknown samples at known positions embedded in a neighbourhood of known samples are discussed. First this restoration problem is treated as a (non-adaptive) 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 neighbourhood of known samples, whereas in general this neighbourhood is infinite. Secondly, for signals that can be modelled as autoregressive processes an adaptive solution to the restoration problem is given.