Ignatjev V.K., Nikitin A.V., Yushanov S.V. About the uniqueness of quasiharmonious representation

Ignatjev Vyacheslav Konstantinovich
 
Doctor of Physics and Mathematics, Professor, Head of Department of Radiophysics, Volgograd State University
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Prospekt Universitetskij, 100, 400062 Volgograd, Russian Federation
 
Nikitin Andrei Viktorovich
 
Candidate of Physics and Mathematics, Associate Professor, Department of Radiophysics, Volgograd State University
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Prospekt Universitetskij, 100, 400062 Volgograd, Russian Federation
 
Yushanov Sergei Vladimirovich
 
Assistant, Department of Radiophysics, Volgograd State University
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Prospekt Universitetskij, 100, 400062 Volgograd, Russian Federation
 
Abstract. It is shown that if for a signal exists quasiharmonious representation with the limited slowly varying frequency, it is unique. It is shown that under condition of a slowness of change of parameters of system, representable in the form of the differential equation of the second order with variable factors, the equation decision exists in the form of quasiharmonious representation with slowly varying amplitude and frequency. It is proposed regularizing algorithm of estimation of parameters of a signal with quasiharmonious representation and a method of estimation of slowly varying factors of the differential equation of the second order. Results of statistical modeling are shown.
 
Key words: quasiharmonic representation, slowly varying parameters, instantaneous frequency, inverse problem, condition of well-posed problem, Tikhonov regularization.

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About the uniqueness of quasiharmonious representation by Ignatjev V.K., Nikitin A.V., Yushanov S.V. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. Issue 13 2010 pp. 137-150
 
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