Approximate methods of solving amplitude-phase problem for continuous signals

Abstract

Amplitude and phase problems in physical research are considered. The construction of methods and algorithms for solving phase and amplitude problems is analyzed without involving additional information about the signal and its spectrum. Mathematical models of the amplitude and phase problems in the case of one-dimensional and two-dimensional continuous signals are proposed and approximate methods for their solution are constructed. The models are based on the use of nonlinear singular and bisingular integral equations. The amplitude and phase problems are modeled by corresponding nonlinear singular and bisingular integral equations defined on the numerical axis (in the one-dimensional case) and on the plane (in the two-dimensional case). To solve the constructed nonlinear singular and bisingular integral equations, spline-collocation methods and the method of mechanical quadratures are used. Systems of nonlinear algebraic equations that arise during the application of these methods are solved by the continuous method of solving nonlinear operator equations. A model example shows the effectiveness of the proposed method for solving the phase problem in the two-dimensional case.