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