Extraction of Pairs of Harmonics from Trigonometric Polynomials by Phase-Amplitude Operators

Extraction of Pairs of Harmonics from Trigonometric Polynomials by Phase-Amplitude Operators DOI 10.1007/s10958-018-3875-0 Journal of Mathematical Sciences, Vol. 232, No. 3, July, 2018 EXTRACTION OF PAIRS OF HARMONICS FROM TRIGONOMETRIC POLYNOMIALS BY PHASE- AMPLITUDE OPERATORS V. I. Danchenko A. G. and N. G. Stoletov Vladimir State University 87, Gor’kogo St., Vladimir 600000, Russia vdanch2012@yandex.ru D. Ya. Danchenko A. G. and N. G. Stoletov Vladimir State University 87, Gor’kogo St., Vladimir 600000, Russia ddanchenko@vlsu.ru UDC 517.53+517.518.86 We propose a method for extracting the sums of two harmonics from trigonometric poly- nomials T (t) by the method of amplitude-phase transformations. Such transformations send polynomials T (t) to similar polynomials by two simplest operations: multiplication by a real constant X and shift by a real phase λ, i.e., T (t) → X · T (t − λ).The n n harmonics are extracted by adding similar polynomials. Bibliography:7 titles. Dedicated to the memory of Vasilii Vasil’evich Zhikov 1 Introduction. Formulation of the Results 1.1. Preliminaries. To extract harmonics from the trigonometric polynomials T (t)= a + τ (t),τ (t):= a cos kt + b sin kt, n ∈ N,a ,b ∈ C, n 0 k k k k k k k=1 we use real amplitude-phase operators of the form T (t) → X · http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Sciences Springer Journals

Extraction of Pairs of Harmonics from Trigonometric Polynomials by Phase-Amplitude Operators

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1072-3374
eISSN
1573-8795
D.O.I.
10.1007/s10958-018-3875-0
Publisher site
See Article on Publisher Site

Abstract

DOI 10.1007/s10958-018-3875-0 Journal of Mathematical Sciences, Vol. 232, No. 3, July, 2018 EXTRACTION OF PAIRS OF HARMONICS FROM TRIGONOMETRIC POLYNOMIALS BY PHASE- AMPLITUDE OPERATORS V. I. Danchenko A. G. and N. G. Stoletov Vladimir State University 87, Gor’kogo St., Vladimir 600000, Russia vdanch2012@yandex.ru D. Ya. Danchenko A. G. and N. G. Stoletov Vladimir State University 87, Gor’kogo St., Vladimir 600000, Russia ddanchenko@vlsu.ru UDC 517.53+517.518.86 We propose a method for extracting the sums of two harmonics from trigonometric poly- nomials T (t) by the method of amplitude-phase transformations. Such transformations send polynomials T (t) to similar polynomials by two simplest operations: multiplication by a real constant X and shift by a real phase λ, i.e., T (t) → X · T (t − λ).The n n harmonics are extracted by adding similar polynomials. Bibliography:7 titles. Dedicated to the memory of Vasilii Vasil’evich Zhikov 1 Introduction. Formulation of the Results 1.1. Preliminaries. To extract harmonics from the trigonometric polynomials T (t)= a + τ (t),τ (t):= a cos kt + b sin kt, n ∈ N,a ,b ∈ C, n 0 k k k k k k k=1 we use real amplitude-phase operators of the form T (t) → X ·

Journal

Journal of Mathematical SciencesSpringer Journals

Published: Jun 2, 2018

References

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