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Signals recovery by the amplitude of its spectrum
https://doi.org/10.32446/0368-1025it.2022-10-44-52
Abstract
A two-stage approximate method for reconstructing the phase of the signal spectrum from the amplitude of the spectrum is proposed. At the first stage, the signal is reconstructed by a numerical method (in one-dimensional and two-dimensional cases) from the known modulus of the spectrum; at the second stage, the spectrum of the reconstructed 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 restoration of one-dimensional and two-dimensional signals are given. The accuracy of signal reconstruction under various perturbations in the input signals and in computational circuits 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.
Keywords
signal recovery,
amplitude-phase problem,
nonlinear Fredholm integral equation of the first kind,
regularization method,
continuous method for solving operator equations
Supporting agencies: the work was supported by Penza State University (competition of research projects “Rector's grants” under Grant no. ХП-221/22 on 31.03.2022).
About the Authors
I. V. Boikov
Penza State University
Russian Federation
Russian Federation
Ilia V. Boikov
Penza
A. A. Pivkina
Penza State University
Russian Federation
Russian Federation
Anastasia A. Pivkina
Penza
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Review
For citations:
Boikov I.V., Pivkina A.A. Signals recovery by the amplitude of its spectrum. Izmeritel`naya Tekhnika. 2022;(10):44-52. (In Russ.) https://doi.org/10.32446/0368-1025it.2022-10-44-52
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