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The implementation of amplitude and phase operator for spectral analysis of harmonic signals

Keywords:

M.Yu. Zvyagin – Ph.D.(Phys.-Math.), Associate Professor, Department of functional analysis and its applications, Vladimir State University named after A.&N. Stoletovs
E-mail: muz1953@yandex.ru
A.S. Golubev – Ph.D.(Eng.), Associate Professor, Department of Physics and Applied Mathematics, Vladimir State University named after A.&N. Stoletovs
E-mail: andrey.golubev@vlsu.ru
D.G. Vasilchenkova – Assistant, Department of functional analysis and its applications, Vladimir State University named after A.&N. Stoletovs
E-mail: darya.vasilchenkova@mail.ru


There are many methods addressing issues associated with spectral analysis of harmonic signal. Most of them are based on integral transforms, and their algorithms are included in a variety of mathematical packages. However, this approach requires the user to have the appropriate software, as well as certain skills to work with it. Hence the idea to implement a simple HTML/JavaScript application, which solves the problem of spectral decomposition of signals. The algorithm is based on the method of Amplitude and Phase Operators (AFO) with exclusively arithmetic nature. It allows to solve the problem without aids of highly specialized mathematical packages and also to improve performance. The essence of the method is the direct overlay of number of similar signals, which differs only in the amplitude and initial phase. Thus, the problem reduces to finding the AFO parameters, i.e. desired amplitudes and phase shifts. Explicit arithmetic formulas for their calculation were obtained in [1]. In the paper we provide code fragments of the demo application, which implement the described algorithm. The application allows you to interactively manipulate the transformation parameters, as well as visualize the result in the form of graphic chart of the original signal and the desired harmonic of given order.

References:
  1. Danchenko V.I., Vasilchenkova D.G. Extraction of harmonics from trigonometric polynomials by amplitude and phase operators. E’lektronny’j resurs: //arXiv:1606.08716v1[math.CA]. 28 Jun 2016. URL = https://arxiv.org/abs/1606.08716.
  2. Prokoshev V.G., Zvyagin M.Yu., Golubev A.S., Kupriyanov A.A. Obrabotka danny’x e’ksperimenta metodom dialogovogo okna // Trudy’ XII mezhd. konf. «Fizika i radioe’lektronika v mediczine i e’kologii». Suzdal’. 5−7 iyulya 2016. Kn. 1. S. 286−289.
  3. Golubev A.S., Zvyagin M.Yu., Samojlova L.I., Kupriyanov A.A. Irregulyarny’e upakovki figur razny’x razmerov i form // Trudy’ XII mezhd. konf. «Fizika i radioe’lektronika v mediczine i e’kologii». Suzdal’. 5−7 iyulya 2016. Kn. 1. S. 289−292.
  4. Golubev A.S., Zvyagin M.Yu., Prokoshev V.G., Samojlova L.I. Irregulyarny’e upakovki figur razny’x razmerov i form // Izvestiya VUZov. Ser. Texnologiya tekstil’noj promy’shlennosti. Ivanovo. 2016. № 5(365). S. 225−231.
  5. Samojlova L.I., Varzin E.I. Povy’shenie kachestva stroitel’stva avtomobil’ny’x dorog / Sb. nauchny’x trudov Mezhdunar. nauch.-prakt. konf. Ch. 1. Transportny’e sistemy’ Sibiri. Krasnoyarsk: Sibirskij federal’ny’j universitet. 2016. S. 211−213.
  6. JavaScript-biblioteka dlya otobrazheniya grafikov i diagramm v veb-brauzerax. URL = http://www.highcharts.com.

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