Approximate Methods for Solving of Onedimensional Amplitude-phase Problem

Abstract

Methods for solving the amplitude-phase problem for one-dimensional signals are proposed. The amplitude-phase problem is investigated in the case of continuous and discrete signals. In both cases, the amplitude-phase problem is modeled by nonlinear singular integral equations. The study of continuous signals leads to nonlinear singular integral equations defined on the numerical axis; discrete ones to nonlinear singular integral equations defined on a unit circle in the plane of a complex variable. The obtained singular integral equations relate to the exceptional case — the symbols of the Frechet derivatives of singular operators degenerate in the entire domain of their definition.The continuous operator method for solution of nonlinear equations is used for solution these nonlinear singular integral equations. The numerical schemes for solving corresponding singular integral equations are constructed. Solutions of model examples have shown effectiveness of the proposed method and numerical algorithms.