Spectral analysis in automated information systems

This article discusses methods of spectral analysis and application in automated information systems, in the frequency domain using the Fourier transform. The authors have developed mathematical models that allow formalizing control and information processing problems in applied areas. The study of the equations proves that the shift of the system in time and the subsequent application of the Fourier transform allows to simplify the analysis of processes and find optimal control actions. The application of spectral methods has made it possible to efficiently find solutions to control problems, especially in the presence of constraints on the system parameters and requirements for the smoothness of the control signal. The obtained expressions demonstrate that the correct choice of the function ũ$^*(\omega)$ taking into account its integrability on the whole frequency axis and finiteness of degree in a given interval allows to carry out accurate and effective control of the dynamic characteristics of the system. The analysis and obtained results show that taking into account these properties of the control function allow to minimize undesirable oscillations, providing smoothness of transient processes and exact compliance with the given boundary conditions. Algorithms of spectral data representation as signal filtering, algorithmic data transformation and time series analysis allowed the authors to highlight or remove certain frequencies in the signal. In existing automated data storage and processing systems, the use of spectral analysis helps to improve the speed of computation.