Reconstruction and Simulation of Experimental Data Using Test Measurements

Abstract—

Mathematical methods for reconstructing the parameters of investigated physical processes from the measurement data of linear time-invariant systems using test signals are proposed and analyzed. The proposed methods are applicable for reconstruction without intermediate determination of the transient response of the system and for simulating the response of measuring systems to a certain excitation. By using the test data, it is possible to dispense with analysis of measuring systems and modeling the measurement process. The regularization of solutions is involved in the reconstruction, which makes it possible to apply the proposed methods to solve ill-conditioned and ill-posed problems. Variants of reconstruction based on direct transformations and integral Fourier transforms are considered and a comparative analysis of these variants and their areas of application is carried out. Cases of data reconstruction in the form of finite and non-finite functions and the corresponding discrete data are analyzed and the discretization errors are estimated. The dependence of the reconstruction error on the noise levels and uncertainties in the initial data is analyzed. The results of numerical experiments on the reconstruction of one-dimensional data and two-dimensional images are presented.