  In various applications the problem of separation of the original signal and
the noise arises. For example, in the identification problem for discrete
linear and causal systems, the original signal consists of the values of
transfer function at some points in the unit disk. In this paper we discuss the
problem of choosing the points in the unite disk, for which it is possible to
remove the additive noise with probability one. Since the transfer function is
analytic in the unite disk, so this problem is related to the uniqueness
theorems for analytic functions. Here we give a new uniqueness result for
bounded analytic functions and show its applications in the denoising problem.
