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Telecommunications and Radio Engineering
SJR: 0.203 SNIP: 0.44 CiteScore™: 1

ISSN Imprimer: 0040-2508
ISSN En ligne: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v55.i10-11.160
6 pages

Solution of Nonlinear Singular Integral Equation Governing Amplitude-Phase Relation in Signal Theory

O.V. Gunko
Kharkov Military University, 6, Svoboda Sq., Kharkov, Ukraine

RÉSUMÉ

On space U of all finite-spectrum signals u = u(t), the integral representation is given to minimum phase solutions of the nonlinear singular integral equation u2 +(H[u]) = A2, where H is the operator of the Hilbert transform describing all signals of the form u(t) = A(t)cos(ω0t + Φ(t) U with the given Hilbert amplitude A = A(t). The representation rests on the basic of Privalov's lemma for a circle and calls for integrability with weight of the function ln A2(t) .


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