### INFORMATION TECHNOLOGIES AND SYSTEMS

DIFFERENTIAL EQUATIONS OF CONTINUOUS COMPLEX FILTERS
Sergey I. Ziatdinov

951

A method to derive differential equation for complex continuous filter using specified frequency transfer function is considered. The method may be applied to low-pass and high-pass filters, band-pass and band-reject continuous complex filters. An equation is presented that relates the spectral densities of the complex input and output signals of the filter with its frequency transfer function. To obtain a differential equation describing the complex filter operation, the inverse Fourier transform is applied to both parts of the equation, so that the input and output signals of the filter are converted from the frequency domain to the time domain. As examples, continuous complex filters of various orders are considered, which at the zero tuning frequency are either low-pass filters or high-pass filters, and at a nonzero tuning frequency, they are either band-pass or notch filters, depending on the specified frequency transfer function type. The differen-tial equations of continuous complex filters are shown to be complex functions of time determined by two quadrature components. To find the transient and impulse characteristics of continuous complex filters, so-lution of the differential equation of low-pass filter (band-pass filter) for a single step input signal is ana-lyzed. The general and particular solutions of the complex differential equation are obtained that determine two quadrature components of the complex transition characteristic of the filter under consideration. By dif-ferentiating the complex transient response, an expression is found for the impulse response of the filter, which is also complex and is represented by two quadrature components.

OBJECTIVE FUNCTIONS AND CONSTRAINTS IN THE PROBLEM OF STRUCTURAL SYNTHESIS OF SYSTEMS FOR COLLECTING AND PROCESSING INF
Shestopalova O. L.

958

Formulation of analytical expressions to describe the objective functions and limitations in the task of finding the optimal structure parameters of distributed two-level information system for collecting and processing information on the technical condition of a spacecraft is considered. The mathematical appa-ratus of the functional-structural synthesis of complex systems is applied, based on multi-criteria discrete programming models. The composition of the generalized vectors of structural parameters of the system and its elements is specified, and formalized expressions for objective functions and constraints are pre-sented.

APPLICATION OF HALSTEAD METRICS FOR QUANTITATIVE ESTIMATION OF COMPUTER PROGRAM CHARACTERISTICS
Aleksey V. Averianov, Igor N. Koshel, Vadim V. Kuznetsov

970

Halstead metrics are applied to statistical characterization of algorithms in programming languages in mnemonic and machine codes. Three programs in mnemonic codes and machine codes are chosen as the studied objects; the programs implement a branching algorithm, an algorithm associated with array pro-cessing, and an algorithm using a subroutine, correspondingly. The derived estimates of the programs length are established to differ significantly from the values obtained as a result of direct analysis of pro-gram texts. It is proved that the transition from programming in mnemonic codes to machine codes in the implementation of algorithms significantly increases the program volume. The lower the level of the pro-gramming language used, the larger the volume of the program, which as a result leads to an increase in the number of potential errors and a decrease in the reliability of software functioning.

ALGORITHM OF AUTOMATIC SELECTION OF COLLOCATIONS FROM THE TEXT
Konstantin V. Nenausnikov, Sergey V. Kuleshov

976

To improve the accuracy of the associative search system, an algorithm for automatic selection of collocations from the corpus of natural language texts is proposed. The developed algorithm is intended for additive estimation of bigrams (pairs of elements) of the text on the basis of statistical approach and selec-tion of the most relevant bigrams with the use of Zipf distribution. Methods of extracting collocations are analyzed on the example of a random corpus of texts obtained from the Internet on the base of such asso-ciative measures as the frequency of occurrence of bigrams in the text - t-test, MI and χ2, using a gram-matical filter, with removal of stop words and subsequent evaluation of these measures. The application of the additive estimation method in the construction of Zipf distribution makes it possible to determine the ar-ea of correct collocations, which leads to a decrease in the number of errors in the obtained collocation lists.

### DEVICES AND SYSTEMS OF AUTOMATIC CONTROL

ERROR OF FIBER-OPTIC GYROSCOPE AT ANGULAR OSCILLATIONS
Аnton V. Miklyashev

982

A fiber-optic gyroscope with rectangular phase modulation and closed feedback is considered. An error formula of this sensor, arising due to the known nonlinearity of the interferometer, is derived. It is shown that the gyroscope error depends on the angular acceleration. Results of simulation modeling are presented, allowing to estimate the admissibility of simplifications made in the derivation of the formula. Ex-perimental confirmation of the obtained dependence is presented for two modifications of the fiber-optic gy-roscope.

COMPLEX OF COMPUTER MODELS FOR STUDYING SEMI-AUTOMATIC CONTROL SYSTEMS OF ROBOT-MANIPULATORS
Ekaterina N. Rostova

989

Semi-automatic control systems of robot-manipulators using various algorithms of control according to vectors of velocity control, position, and force of the robot gripper that correspond to technological oper-ations performed by robot-manipulators, are considered. A complex of computer models for the investiga-tion of the control systems under consideration is developed. The algorithms schematics are demonstrated and units of the computer models for studying open-loop and closed-loop control systems are described. Results of modeling of semi-automatic systems for control by velocity vector assigned by the human operator are presented. Recommendations for application the developed complex of models for training operators of semi-automatic control systems for robot-manipulators are given.

MEASURING CIRCUITS OF DIRECT CONVERSION FOR CAPACITIVE ACCELEROMETERS AND GYROSCOPES
Arbuzov Viktor P.

997

Measuring circuits of differential capacitive parametric converters intended for taking information about inertial mass oscillations of accelerometers or gyroscopes are considered. Error analysis of the measuring circuit based on operational amplifier is carried out, and ways of reduction of each of the con-sidered components of the resulting error are outlined. Schematics of measuring circuits providing trans-formation of informative parameter of the differential capacitive sensor and correction of the error caused by imperfection of the operational amplifier are presented. It is noted that the scope of measurement cir-cuits without an operational amplifier is limited by a narrow range of working capacitance; structures built on an operational amplifier have a linear conversion function regardless of the deviation of the working ca-pacitance.

### OPTICAL AND OPTO-ELECTRONIC INSTRUMENTS AND SYSTEMS

ANALYSIS OF THE CONVERSION ACCURACY OF THE COLOR SATURATION IN MODERN SOFTWARE
Mikhail V. Belodedov, Nikolay M. Zotov, Aleksandеr V. Khoperskov, Alexey M. Chmutin, Vladimir Chuiko

1005

Color saturation control tools of modern computer graphics software is analyzed. For the case of a virtual instrumentation, the concomitant error is defined as a three-dimensional value, and a classification of the error components is proposed. Two new shift-type components are introduced, and their properties are studied using sampling from 24 software packages. The criticality of one of the error components, threatening the integrity of visual information in the process of contrast transformation, is revealed. It is shown that the existing tools are not able to provide systemic color saturation contrast control, and this lim-its their application area to the tasks of image synthesis only.

METHOD OF MEASUREMENT OF SPECTRAL EMISSIVITY OF HEATED BODIES
Vyacheslav P. Hodunkov

1015

A new spectral method for measuring the emissivity of solids at high temperatures is considered. The method is based on determination of wavelength dependence of the studied body spectral brightness in a narrow spectral range. Theoretical substantiation and results of experimental verification of the method are presented.

### SCIENTIFIC AND PRACTICAL DEVELOPMENTS

INSTALLATION FOR MEASURING THERMOPHYSICAL PROPERTIES
OF HEAT-INSULATING MATERIALS BY METHODS OF LINEAR AND PLANAR PULSED HEAT SOURCES
Valentina O. Bulanova, Evgeny V. Bulanov, Sergey V. Ponomarev, Alexander G. Divin

1022

An installation for measurement of thermophysical properties of heat-insulating materials is presented. Using the methods of linear and planar pulsed heat sources, mathematical models of relative errors in the measurement of bulk heat capacity and the coefficient of thermal conductivity of solid materials are developed, a method for determining the optimal conditions for processing experimental data, choosing the main structural size of measuring devices and the optimal duration of thermal pulses is created. A software of information-measuring system is described.

### BRIEF NOTES

TEST BENCH FOR SYNCHRONOUS BRUSHLESS MOTOR
Silaev Alexey A., Marusina Maria Ya., Denis A. Nevmerzhitsky

1030

Several features of the design of the executive mechanism of the load stand for testing engines are considered. A magnetic coupling is used to measure torque and rotational speed. Parameters of the magnet-ic coupling as well as of the motor-generator used as the load device, are calculated using the finite element method. Based on presented results of numerical modeling, the main characteristics of the stand are ob-tained.