Article is prepared for printing L. I. Zolotinkina, is printed with some reductions concerning generally of the mathematical calculations confirming theoretical results of scientific researches I. G. Freymana. Reflection still of very important direction of works of I. G. Freyman connected with use of electrovacuum devices. In a number of its articles for the first time in domestic technical literature questions of terminology and determination of the main sizes characterizing operation of "hollow devices" were considered, methods of an assessment of quality of electron tubes are theoretically proved and offered. More than 60 publications and books are included into the list of scientific works of professor Freyman, practically all of them were the first scientific works in a number of the new scientific directions created as a result of development of radio engineering, considering the first publication - article A. S. Popova (1895).

Receiving of the broadband phase modulated signal with quadrature phase-shift keying in case of multiple access in-terference and internal Gaussian noise has been considered. Bit error rate of broadband phase modulated signal with quadrature phase-shift keying has been obtained in case amplitudes of receiving signal and interferences have both regu-lar and fluctuating components. Broadband phase modulated signal bit error rate as a function of signal-to-noise ratio, signal-to-interference ratio, number of interferences and false positive probability has been analyzed.

Methods of identification and recognition of sonar signals reflected from the bodies with complex geometric shape have been developed and calibrated in hydroacoustic tank and at sea. Their greater noise immunity is achieved in comparison with well-known recognition methods. Comparison of these methods with wave front reversal method is given. Simulation results help to explain well-known fact that dolphins use multiple impulse sounding transmission with unequal interpulse periods.

The results of statistical analysis of neural network tuning by LMS-algorithm with square constraint for weight vector jitter are represented. The expressions for correlation function of output signal of neuron of the neural of different network layers are obtained. It is shown, that the weight vector jitter leads to distortions of statistical characteristics of neural network and these distortions increase with increasing of number of neural network layer.

Expressions for an assessment of efficiency of the damping filters of the third order in power networks are received. On the basis of these expressions graphic dependences at various parameters of filters are given.

Two-channel continuous and discrete transformation of a signal at various pulse characteristics of the converter in television fields is considered. The expressions allowing to calculate characteristics of the restoring filters providing un-distorted transfer of an entrance signal are received.

There is usage of the processing of nonlinear frequency signals considered to reduce the losses of the detection. The efficiency of a nonlinear frequency signal detector width multichannel filter it is valued in range of the Doppler fre-quencies.

In clause is considered principle construction net of telemechanics for object of electric power on base wireless link. Adduce of criterion choice the route, written the algorithm of construction the route on example real net. Considered automatic form the new station of control in net.

Deterioration maximum range and accuracy of measurement range and angular coordinates caused by energy losses during processing phase manipulated radio signals is considered. It has been shown that a decrease of energy losses is possible by using a phase-manipulated signals with smoothly changing phase between the elementary pulses.

Configuration of the radar system circular view for vehicles based on ultra-wideband sensors is proposed. The algorithms of coordinate determination are considered. The estimations of coordinate measurement accuracy are obtained.

The solution of a problem of identification of the current coordinates of navigation satellites together with definition of errors of mutual synchronization of their hours directly onboard the satellite on the basis of use of simple methods of inter-satellite radio - and laser measurements is considered.

Modern methods and means of measurement used in the Russian digital terrestrial television networks are considered. New methods for improving the efficiency and objectivity of measurements in digital television proposed.