• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Introduction to signal processing: information transmission using orthogonal sine waves
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
September 15, 2026
Immunity to Chaos: How Personal Resources Help Us Cope with the Challenges of a Turbulent World
International conflicts, crises and digital overload—the modern world puts our minds to the test every day. Traditional psychology often focuses on the consequences: anxiety, depression, and psychosomatic disorders. But what if we looked at the problem differently—through the lens of the resources that prevent us from breaking down? Psychological immunity is precisely this set of resources. Alena Zolotareva and her group, Psychological Immunity as a Resource for Positive Functioning, are developing an integrative model of this phenomenon, adapting diagnostic tools and preparing for large-scale empirical research. Why do psychologists need to collaborate with medical professionals, and how could their research transform preventive care in clinics and corporations?
September 11, 2026
How to Assess Students Knowledge in the Age of AI
A researcher at HSE University has proposed a flowchart to help lecturers decide how to assess students who use artificial intelligence. It shows where the use of AI should be restricted and where it can be incorporated into the learning process. The article has been published in IT Professional.
September 9, 2026
‘Balkan Hospitality Opens Doors: Studying Dialects on the Verge of Extinction
You cannot study spoken dialects from books. Instead, you need to go to a village, seek out its elders, and earn the trust of local residents before you can record hours of spontaneous stories. This is how Natalia Muravleva, Associate Professor at the Faculty of Humanities, conducts her research. Her internship in Serbia continued her long-standing study of dialects spoken by Macedonian settlers. In this interview, she discusses how diaspora cultural centres help researchers reach informants, why native speakers need to be interviewed only in their own language (otherwise, as she puts it, they may 'break'), and how a single field season helped her finalise her monograph. She also shares warm memories of autumn in Belgrade and of colleagues with whom grammar can be discussed in three languages at once.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Introduction to signal processing: information transmission using orthogonal sine waves

International Journal of Open Information Technologies. 2020. Vol. 8. No. 6. P. 51–42.
Tikhonov E., Sneps-Sneppe M.

Data transmission using orthogonal functions means combining base carrier signals (scaled by numbers of useful information) into one sent signal. Processing the mixed signal after receiving allows dividing it back into carriers and restoring useful numbers.
What is the most compact set of complex sine waves for this? How will the random components of the spectrum between the system signals (or the imperfection of the parameters) affect the result? What is the algorithm for processing the received signal and what is the minimum time needed to obtain the initial information? These issues are discussed “from the bottom to up”, from simple physical considerations to mathematical expressions and processing algorithms in the MatLab package.

Language: English
Full text
Text on another site
Keywords: ряды Фурьескалярное произведениеcomplex signalсистема MATLABMATLAB Fourier seriesdiscrete Fourier transformscalar productsine wavecomplex sine wavesсинусоидальная волнакомплексный сигналдискретное преобразование Фурье
Similar publications
Об интегрируемости динамических систем в пространстве двусторонних последовательностей
Рассадин А. Э., Журнал Средневолжского математического общества 2026 No. 2 P. 26–48
The article is devoted to the analysis of dynamical systems in a specially constructed counting phase space, namely, in the space of bilateral sequences. It is not only a linear space but also a Banach algebra. Using the multiplication operation in this algebra, the article constructs two examples of dynamical systems in such a space, ...
Added: April 29, 2026
Дискретный аналог формулы суммирования Пуассона
Ustinov A., Математические заметки 2003 Т. 73 № 1 С. 106–112
The first part of this paper is concerned with the proof of a discrete analog of the Poisson summation formula. In the second part, we describe an elementary proof of a functional equation for the function θ(t), based on the summation formula derived in the paper. ...
Added: October 11, 2025
Вычисление суммы Гаусса с помощью дискретного преобразования Фурье
Ustinov A., Дальневосточный математический журнал 2014 Т. 14 № 1 С. 90–95
The explicit formula for a Gauss sum is proved using the discrete Fourier transform. The Gauss quadratic reciprocity law is established as a corollary. ...
Added: October 9, 2025
Механические характеристики модели молекулярной динамики и полиномы Коробова
Ustinov A., Гузев М. А., Дальневосточный математический журнал 2016 Т. 16 № 1 С. 39–43
We use the number theory methods for explicit calculation of a static stress field in the system of a 1D chain harmonic oscillators. The sums defining stress field are presented in terms of Korobov polynomials for arbitrary number of oscillators and arbitrary averaging scale. ...
Added: October 9, 2025
Lp-estimates for scalar products of vector fields and their application to electromagnetic theory problems
Tyukhtina A. A., Kalinin A., Mathematical Methods in the Applied Sciences 2018 No. № № 18. V. 41 P. 9283–9292
Added: September 22, 2023
The discrete Fourier transform over the binary finite field
Sergei Valentinovich Fedorenko, IEEE Access 2023 Vol. 11 P. 62771–62779
The novel methods for binary discrete Fourier transform (DFT) computation over the finite field have been proposed. The methods are based on a binary trace calculation over the finite field and use the cyclotomic DFT. The direct DFT computational complexity has been reduced due to using the binary trace function over the finite field and ...
Added: July 19, 2023
Cyclostationary Approach to the Analysis of the Power in Electric Circuits under Periodic Excitations
Shevgunov T., Guschina O., Kuznetsov Y., Applied Sciences (Switzerland) 2021 Vol. 11 No. 20 Article 9711
This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving ...
Added: February 6, 2023
О переносе ряда понятий статистической радиофизики в теорию одномерных точечных отображений
Агаларов А. М., Потапов А. А., Рассадин А. Э. et al., Моделирование и анализ информационных систем 2018 Т. 25 № 1 С. 7–17
In the article, the possibility of using a bispectrum under the investigation of regular and chaotic behaviour of one-dimensional point mappings is discussed. The effectiveness of the transfer of this concept to nonlinear dynamics was demonstrated by an example of the Feigenbaum mapping. Also in the work, the application of the Kullback-Leibler entropy in the ...
Added: December 17, 2022
A spectral algorithm for decoding systematic BCH codes
Fedorenko Sergei Valentinovich, IEEE Access 2022 Vol. 10 P. 110639–110645
A novel method of spectral decoding for systematic BCH codes has been proposed. This method has a simple description and a small computational complexity. ...
Added: October 26, 2022
Короткое доказательство тождества Ландсберга–Шаара
Ustinov A., Математические заметки 2022 Т. 112 № 3 С. 478–480
In the paper we proposes a new short proof of the Landsberg-Schaar identity based on finite Fourier series. ...
Added: October 10, 2022
BLUETOOTH 5.1 INDOOR LOCALIZATION STUDY BASED ON ANGLE-OF-ARRIVAL METHOD
Sviatoslav Iakimenko, Tsislav A., Naumova E. et al., Telecommunications and Radio Engineering (США) 2022 Vol. 81 No. 3 P. 51–61
Bluetooth 5.1 is a new technology with a sample of novel features. One of the most significant improvements compared to the previous version is in the enhancement of indoor localization with techniques such as angle of departure (AoD) and angle of arrival (AoA). Up to date, only a modest number of limited practical studies were ...
Added: August 10, 2022
Sequential analysis in Fourier probabilistic neural networks
Savchenko A., Belova N. S., Expert Systems with Applications 2022 Vol. 207 Article 117885
In this paper, the computational complexity of the probabilistic neural network for the classification of high-dimensional data is improved. At first, the class probability densities are estimated by using only a few principal components of an observed point. The Gaussian–Parzen kernel is replaced by the orthogonal series estimates of class-conditional densities for each principal component using the Fourier series to speed ...
Added: June 29, 2022
Introduction to signal processing: sine wave and complex signals
Tikhonov E., Sneps-Sneppe M., International Journal of Open Information Technologies 2019 Vol. 7 No. 3 P. 17–24
The article describes one of the powerful tools for the signals analysis while transmission – complex mathematics. Here the basic concepts (complex numbers, complex signal as expansion of a real signal to a complex-valued function) and some operations (exponentiation, absolute value and angular phase representation) are introduced. As an example complex mathematical methods are used for ...
Added: April 9, 2022
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit