The optimal measurement problem for the measurement transducer model with a deterministic multiplicative effect and inertia

The results of the theory of Sobolev-type equations are extensively used to measure of dynamically distorted signals recently. In this paper the authors consider the optimal measurement for the system where the well-known multiplicative effect was produced which in its turn has the form of a scalar function of the variable t. The authors develop the exact and approximate solutions of the optimal measurement problem for the specified system. The paper consists of two parts. The statement of the problem is formulated in the first part as an optimal measurement for the system with a deterministic multiplicative effect, and the second part presents the formulas of exact and approximate solutions of the problem.