The mathematical description of the functional transformations of a signal with angular modulation in sequentially the connected quantizers of a phase and tension

The most important constituent of the modern terrestrial stations of satellite communication are digital synthesizers of signals. With their help various composite signals indicators. The interest of developers in use in the created and perspective terrestrial stations of satellite communication of digital synthesizers of signals is caused by a number of the objective reasons: – digital synthesizers of signals, in comparison with analog, have high stability of parameters of the formed signals and low level of phase noise; – the combination of broad functionality to high speed of switching and a small step of reorganization on the frequency (a share of hertz) allows to form with use of the same device signals of various frequency with a high precision of installation and speed of switching; – the quick action of the modern element base allows to form heterodyne signals in the wide working range of frequencies making hundreds of megacycles. Enough scientific works is devoted to a research of methods and devices of digital formation of different types of signals. Digital synthesizers of signals with angular modulation are considered in them insufficiently fully, as a rule, separately from each other, without identification of common for them regularities and features of the analysis. The analysis of transformations of the digital signal with angular modulation in digital synthesizers of signals presented by function of several variables, as a rule, is based on numerical methods. For its carrying out it is necessary to receive the mathematical description of transformations of signals with angular modulation in an analytical look. The functional dependences describing transformations of signals with angular modulation in sequentially the connected quantizers of a phase and tension with use of a method of display of signals and a method of planimetric integrals are presented in article. The received dependences allow to estimate distortions of the formed signal by means of spectral and correlation analysis.