Numerical solution of the Hilbert transform for phase calculation from an amplitude spectrum

Andersson, Torbjörn; Johansson, Jan M.; Eklund, H.

doi:10.1016/0378-4754(81)90082-3

Cited by 8 publications

(1 citation statement)

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“…Usually such quadrature formulae have been developed taking into account that the integrand is a polynomial or spline function [10], [11], but this is not always the case in practical situations (Section IV). A widespread used method for numerical computation of integrals is the Gaussian quadrature, where the weights and abscissa values can be determined so that the quadrature is exact for integrand of the form f (τ ) = w(τ )P (τ ), where P (τ ) is a polynomial and w(τ ) is a weight function.…”

Section: Gaussian Quadraturementioning

confidence: 99%

Gain-phase relationships evaluation by Gaussian quadrature

Rusu

Grama

2008

2008 International Conference on Signals and Electronic Systems

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Hilbert transform has been recognized as a very important method in circuit theory, communications and control science. Its sampled derivations have been encountered in different applications from science and engineering. In this paper, the gain-phase relationships are evaluated using Gaussian quadrature. First we recall the Hilbert transform and a part of the theoretical background of the Gaussian quadrature approach. The approximation of the Hilbert transform with Gaussian quadrature is described and examples of gain-phase relationships are presented. Finally we discuss the advantages and drawbacks of this Gaussian approach.

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Section: Gaussian Quadraturementioning

confidence: 99%