Information Technology of the Fourier-Integral Identification Method Implementation for Recovery of Input Signals of Information and Measurement Systems

Abstract

Information technology for implementing the Fourier integral identification method for restoring input signals of information and measuring systems from their output signals, created in the 1980s by B. I. Mokin and generalized by O. B. Mokin, has been developed. The developed information technology is based on a computer program created in the Python language. The first part of this Python program restores the input signal of the information and measuring system from its output signal in the form of a truncated Fourier series, which causes the appearance of drops on the graph of this restored input signal, due to the finite number of restored harmonic components. The second part of the Python program transforms the truncated Fourier series into a Fourier series with an infinite number of harmonic components, i.e., it forms an equivalent model of the input series, cleaned of the differences caused by the finite number of restored harmonic components. With appropriate justification, the transformation of the truncated Fourier series into a Fourier series with an infinite number of harmonic components was carried out using a nonlinear variant of the least squares method. In the process of implementing the Python program, it was demonstrated how the dynamic characteristics of information and measuring systems affect the output signals of these systems, which was confirmed both by calculations and graphically, and is a confirmation of the need to supplement information and measuring systems with information technologies for restoring their input signals from their output signals with the structure proposed in this article. The results obtained were analyzed and solutions were proposed, according to which the structure of the proposed information technology and the structure of the Python program, which is the basis of this information technology, can be brought into line with other conditions for the functioning of information and measuring system, the input signal of which is restored from its output signal.