Error-Free Filtering of an Entropy-Singular Signal under Independent Distortions

The problem of filtering for a discrete-time stationary stochastic process $X=\{X_n\}$ from observations $Y=\{Y_n\}$ in the case of independent distortions satisfying the natural condition of dependence on the signal being estimated is considered. It is shown that for an entropy-singular process $X=\{X_n\}$ the value of $X_n$ at any time instant n can be reconstructed without error from the observations $\{Y_j, j \leq m\}$ for any $m$.