Exact Moment Simulation Using Random Orthogonal Matrices

Introduction: The problem of noise-free encoding for an open radio channel is of great importance for data transfer. The results presented in this paper are aimed at stimulating scientific interest in new codes and bases derived from quasi-orthogonal matrices, as a basis for the revision of signal processing algorithms.Purpose: Search for new code sequences as combinations of codes formed from the rows of Mersenne and Raghavarao quasi-orthogonal matrices, as well as complex and more efficient Barker — Mersenne — Raghavarao codes.Results: We studied nested code sequences derived from the rows of quasi-orthogonal cyclic matrices of Mersenne, Raghavarao and Hadamard, providing estimates for the characteristics of the autocorrelation function of nested Barker, Mersenne and Raghavarao codes, and their combinations: in particular, the ratio between the main peak and the maximum positive and negative “side lobes”. We have synthesized new codes, including nested ones, formed on the basis of quasi-orthogonal matrices with better characteristics than the known Barker codes and their nested constructions. The results are significant, as this research influences the establishment and development of methods for isolation, detection and processing of useful information. The results of the work have a long aftermath because new original code synthesis methods need to be studied, modified, generalized and expanded for new application fields.Practical relevance: The practical application of the obtained results guarantees an increase in accuracy of location systems, and detection of a useful signal in noisy background. In particular, these results can be used in radar systems with high distance resolution, when detecting physical objects, including hidden ones.

Download Full-text

Circles on lattices and Hadamard matrices

Information and Control Systems ◽

10.31799/1684-8853-2019-3-2-9 ◽

2019 ◽

pp. 2-9 ◽

Cited By ~ 1

Author(s):

N. A. Balonin ◽

M. B. Sergeev ◽

J. Seberry ◽

O. I. Sinitsyna

Keyword(s):

Hadamard Matrices ◽

Lattice Points ◽

Practical Significance ◽

Upper And Lower Bounds ◽

Problem Size ◽

Orthogonal Matrices ◽

Video Information ◽

Scientific Schools ◽

Gauss Theorem ◽

Triangular Numbers

Introduction: The Hadamard conjecture about the existence of Hadamard matrices in all orders multiple of 4, and the Gauss problem about the number of points in a circle are among the most important turning points in the development of mathematics. They both stimulated the development of scientific schools around the world with an immense amount of works. There are substantiations that these scientific problems are deeply connected. The number of Gaussian points (Z3 lattice points) on a spheroid, cone, paraboloid or parabola, along with their location, determines the number and types of Hadamard matrices.Purpose: Specification of the upper and lower bounds for the number of Gaussian points (with odd coordinates) on a spheroid depending on the problem size, in order to specify the Gauss theorem (about the solvability of quadratic problems in triangular numbers by projections onto the Liouville plane) with estimates for the case of Hadamard matrices. Methods: The authors, in addition to their previous ideas about proving the Hadamard conjecture on the base of a one-to-one correspondence between orthogonal matrices and Gaussian points, propose one more way, using the properties of generalized circles on Z3 .Results: It is proved that for a spheroid, the lower bound of all Gaussian points with odd coordinates is equal to the equator radius R, the upper limit of the points located above the equator is equal to the length of this equator L=2πR, and the total number of points is limited to 2L. Due to the spheroid symmetry in the sector with positive coordinates (octant), this gives the values of R/8 and L/4. Thus, the number of Gaussian points with odd coordinates does not exceed the border perimeter and is no less than the relative share of the sector in the total volume of the figure.Practical significance: Hadamard matrices associated with lattice points have a direct practical significance for noise-resistant coding, compression and masking of video information.

Download Full-text

TECHNICAL AND ECONOMIC EVALUATION OF THE DEVELOPMENT OF A DEVICE FOR THE PREVENTION OF APNEA DURING PHYSIOLOGICAL SLEEP IN HUMANS

СИСТЕМНЫЙ АНАЛИЗ И УПРАВЛЕНИЕ В БИОМЕДИЦИНСКИХ СИСТЕМАХ ◽

10.36622/vstu.2020.19.3.025 ◽

2020 ◽

pp. 198-210

Author(s):

Сергей Борисович Казаков ◽

Дмитрий Михайлович Шишов ◽

Антон Игоревич Ларин ◽

Александр Петрович Николаев ◽

Аза Валерьевна Писарева

Keyword(s):

Sleep Apnea ◽

Humidity Sensor ◽

Lung Ventilation ◽

High Price ◽

Device Structure ◽

Artificial Lung Ventilation ◽

Exact Moment ◽

The Cost ◽

Technical Solutions ◽

Physiological Sleep

В статье представлен обзор существующих технических решений в сфере мониторинга и предотвращения апноэ во сне. Произведён анализ существующих аппаратов для предотвращения апноэ, который показал, что на рынке присутствует большое количество импортных моделей, однако они имеют довольно высокую цену. Разработанный нами Российский аналог проектируемого аппарата, при схожих характеристиках, будет иметь более привлекательную цену, чем у импортных приборов. Интегрирование датчика влажности в персональную маску пациента даёт возможность отслеживать остановки дыхания пациента во время сна, и тем самым включать процесс принудительной подачи дыхательной смеси именно в тот момент, когда она необходима для устранения патологии. Целью научной работы является разработка конструкции прибора и создание алгоритма программы для управления аппарата искусственной вентиляции лёгких для предотвращения апноэ во сне. Показана разработка структуры устройства аппарата. Подобран компрессор и датчик влажности с обоснованными характеристиками для создания аппарата, а также основные элементы. Разработана конструкция корпуса аппарата и разработана компоновка. Выполнено технико-экономическое обоснование разработки аппаратно-программного комплекса для предотвращения апноэ во сне. Показано, что себестоимость готового изделия достаточно конкурентна The article presents an overview of existing technical solutions in the field of monitoring and prevention of sleep apnea. An analysis of existing devices for preventing apnea was made, which showed that there are a large number of imported models on the market, but they have a fairly high price. The Russian analog of the designed device developed by us, with similar characteristics, will have a more attractive price than that of imported devices. The integration of the humidity sensor into the patient's personal mask makes it possible to monitor the patient's breathing stops during sleep, and thus enable the process of forced delivery of the respiratory mixture at the exact moment when it is necessary to eliminate the pathology. The purpose of the research is to develop the device design and create a program algorithm for controlling the artificial lung ventilation device to prevent sleep apnea. The development of the device structure is shown. The compressor and humidity sensor with reasonable characteristics for creating the device, as well as the main elements are selected. The design of the device body and its layout were developed. A feasibility study for the development of a hardware and software system for preventing sleep apnea has been completed. It is shown that the cost of the finished product is quite competitive

Download Full-text

Turning Dynamics: Part 1 — Experimental Analysis

Volume 4: Dynamics, Control and Uncertainty, Parts A and B ◽

10.1115/imece2012-87933 ◽

2012 ◽

Author(s):

Eric B. Halfmann ◽

C. Steve Suh ◽

N. P. Hung

Keyword(s):

Instantaneous Frequency ◽

Period Doubling ◽

Displacement Sensor ◽

Laser Displacement Sensor ◽

Turning Process ◽

Time Frequency ◽

Spectral Components ◽

Tool Vibrations ◽

Exact Moment ◽

The Stability

The workpiece and tool vibrations in a lathe are experimentally studied to establish improved understanding of cutting dynamics that would support efforts in exceeding the current limits of the turning process. A Keyence laser displacement sensor is employed to monitor the workpiece and tool vibrations during chatter-free and chatter cutting. A procedure is developed that utilizes instantaneous frequency (IF) to identify the modes related to measurement noise and those innate of the cutting process. Instantaneous frequency is shown to thoroughly characterize the underlying turning dynamics and identify the exact moment in time when chatter fully developed. That IF provides the needed resolution for identifying the onset of chatter suggests that the stability of the process should be monitored in the time-frequency domain to effectively detect and characterize machining instability. It is determined that for the cutting tests performed chatters of the workpiece and tool are associated with the changing of the spectral components and more specifically period-doubling bifurcation. The analysis presented provides a view of the underlying dynamics of the lathe process which has not been experimentally observed before.

Download Full-text