Different Approaches to Studying the Extreme Properties of Signal Functions Synthesized with Splines

Abstract

The study of parameters of the full energy of signal functions, which are built on the basis of square spline functions,with the use of various evaluation criteria, was conducted. The use of the coefficient of energy concentration (energy criterion) of signals based on quadratic splines is proposed, an analytical equation is obtained for a selective signal whose energy is concentrated near the main lobe, allowing you to choose the optimal values of the width parameter of the transition region and the shape of the spectrum signal implementations. The use of the D-criterion for signals with a limited duration and intersymbol interference is considered. It is shown that the minimization of the level of interference is possible due to the variation of the parameter of the signal spectrum in the transition region, allowing the synthesis of signals with the necessary properties during practical implementation. The use of the criterion of the size of the eye-diagrams allowed us to synthesize signals that are most resistant to shifts of the moments of sampling—jitter. The conditions under which the maximum value of the opening is reached are determined. It was established that in the research of the full energy selective signal evaluation criterion appropriate to use with differential calculus function of several variables, which allows the network in step predetermined design technology to provide the required energy signal indicators. As a result, the use of various criteria for the research of the parameters signals makes it possible at the design stage of signals of mobile communication networks to synthesize such forms that will allow them to physically fully realize them in practice, thereby improving the characteristics of the radio link equipment.