Bukhan D. Development of methods for analysis and synthesis of signals with compact spectrum

3. The object is in processes of transformation of informational signals in telecommunication systems. The subject is in methods of analysis and synthesis of signals with compact spectrum. Research methods: methods of approximation theory (in development the mathematical model of selective signals with random number of parameters), methods of optimization theory (in solving tasks of synthesis selective and partial signals), methods of theory of orthogonal transformation and spectral analysis (in obtaining analytical expressions for multiparameteric signal functions in timed form), mathematical modeling and simulations on a computer (in calculating different characteristics of selective and partial signals). Theoretical and practical results: the new criteria for comparing selective signals are proposed. The criteria are based on methods of receiving and transmitting corresponding signals. The method for defining limit values of energy concentration on given time interval has been developed. A new method of synthesis selective signals is proposed. The method is based on increasing number of degrees of freedom in a signal function, when this function is described by spline with big number of nodes. The limit values of energy concentration of multiparameteric selective signals has been founded for the first time. A new method of synthesis multiparametric partial signals is proposed. The main point of the method is in using multiparametric selective signals to create partial ones based on them. The set of algorithms has been developed, and corresponding programs have been written to build eye-patterns of partial signals with distortions, to calculate vertical and horizontal apertures of the eye-pattern, generalized D and E-criteria, numerical optimization of multiparametric functions (using Nelder-Mead’s method). The relation between value of channel’s AFR and aperture of an eye-pattern has been founded. The criterion for the quantitative assessment of time-frequency localization’s degree of signal functions has been explicated. The method of substantiating signal choosing for channel with known maximum value of distortions has been offered.