Uniqueness theorem for analytic functions and its application in denoising problem

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.