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Telecommunications and Radio Engineering
SJR: 0.202 SNIP: 0.2 CiteScore™: 0.23

ISSN 印刷: 0040-2508
ISSN オンライン: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v57.i4.100
13 pages

Integral Representation of Solutions to the Non-Linear Singular Integral Equation Governing Amplitude-Phase Relations in the Communication Theory

O. V. Gunko
Kharkov State Technical University of Radio Engineering and Electronics, 14, Lenin Ave, Kharkov, 61166, Ukraine

要約

In the space U of all signals u = u(t) with compact-carrier spectra, an integral representation has been obtained for minimum-phase solutions of the non-linear singular integral equation u2 + (Hu)2 = A2, where H is the Hilbert transformation operator. The equation describes all signals of the form u(t) = A(t)cos(ω0t + Φ(t)) U that correspond to the given Hilbertian amplitude A = A(t). The representation is derived, based on Privalov's fundamental lemma for the circle and proof of weighted integrability for the function ln A2(t).


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