RT Journal Article ID 49ad9b155a306887 A1 Gunko, O. V. T1 Integral Representation of Solutions to the Non-Linear Singular Integral Equation Governing Amplitude-Phase Relations in the Communication Theory JF Telecommunications and Radio Engineering JO TRE YR 2002 FD 2002-04-01 VO 57 IS 4 OP 13 AB 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). PB Begell House LK https://www.dl.begellhouse.com/journals/0632a9d54950b268,5f37389b56aa78ad,49ad9b155a306887.html