# A method and a program for the numerical evaluation of the Hilbert transform of a real function

## Description

Abstract In the first part of this paper a method for the evaluation of the Hilbert transform of a function, approximated by piecewise polynomials, is presented. In the second part a program is presented to be used when the function is approximated by cubic splines. We show that the Hilbert transform displays the same strong convergence properties as the cubic splines. The asymptotic properties of the Hilbert transform are shown to be very well reproduced. Title of program: FHT Catalogue Id: ABVD_v1_0 Nature of problem This program calculates the Hilbert transform of a continuous function. The evaluation of the matrix elements of the Green's function in quantum mechanics involves the evaluation of the Hilbert transform of the matrix elements of the Hamiltonian operator. The same type of problem appears in many other fields of applied physics. The program assumes that a cubic spline interpolation has been performed over the integration region. As the Hilbert transform function is evaluated at a point of the com ... Versions of this program held in the CPC repository in Mendeley Data ABVD_v1_0; FHT; 10.1016/0010-4655(80)90008-9 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)