Signals Recovery by the Amplitude of the Spectrum

A two-stage approximate method for recovering the phase of the signal spectrum from the amplitude of the spectrum is proposed. In the first stage, the signal is recovered by a numerical method (in the one-dimensional and two-dimensional cases) from the known modulus of the spectrum; in the second stage, the spectrum of the recovered signal is determined and the phase of the spectrum is calculated. signal recovery from a known modulus of the spectrum is modeled by a nonlinear Fredholm equation of the first kind, which is solved using the spline-collocation method with splines of zero and first orders and a generalization of the continuous method for solving nonlinear operator equations. Model examples of the recovery of one-dimensional and two-dimensional signals are given. The accuracy of signal recovery for various perturbations in the input signals and in computational frameworks has been studied. The absolute and relative values of spikes at the leading and trailing edges of the signals are estimated. methods for suppressing the Gibbs effect are considered. The proposed method can be used in optics, astrophysics, biology, and medicine.