THE COMPATIBLE DESCRIPTION OF SIGNALS, LINEAR LINKS AND RESPONSES OF TELECOMMUNICATIONS AND RADIOELECTRONICS SYSTEMS

Mathematical modeling is a basic tool for design and development of modern telecommunications and radioelectronics systems. It is realized on two fundamentally different levels: schematic circuit and block diagram simulation. At the initial stages of design and development of system (i.e. research scientific work, specification of requirements, initial outlay and technical project) simulation on the block diagram level is applied. Its results define the structure and basic parameters of the quality of created facilities. It has been established, that commonly applied software of block diagram simulation has essential flaws, which are resulted from a scarce mathematical description of signals and links. The research described in the article is aimed at working out the mathematical description of signals, linear links and responses. This description will contribute to creating the enhanced library of mathematical models of signals and linear links, as well as automated procedures of formation, transformation and calculation of time-and-frequency characteristics of signals, links and responses.

We suggest a mathematical description of signals, linear links and responses on the basis of specifically shaped operator fractional-rational function. It embodies and epitomizes all types of signals, linear links and responses used in modeling and provides needed transformation and creation of the enhanced library of mathematical models of signals and linear links. Subsequently, it allows creation of mathematical algorithms of normalization, reactance transformation and multiplication of models of minimum-phase and nonminimum-phase linear links, as well as generalized models of signals, linear links and responses in frequency- and time-domains. These generalized models make a basis of single mathematical algorithms and automated procedures of calculation frequency- and time-characteristics of signals, links and responses. 

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