Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach

The numerical evaluation of Hilbert transforms on the real line for functions that exhibit oscillatory behavior is investigated. A fairly robust numerical procedure is developed that is based on the use of convergence accelerator techniques. Several different types of oscillatory behavior are examin...

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Bibliographic Details
Published in:Computer physics communications 2002-05, Vol.145 (2), p.256-266
Main Authors: King, Frederick W., Smethells, Gregory J., Helleloid, Geir T., Pelzl, Paul J.
Format: Article
Language:English
Subjects:
Convergence acceleration
Exact sciences and technology
Function theory, analysis
Hilbert transforms
Integral transforms and operational calculus
Mathematical methods in physics
Numerical approximation and analysis
Numerical differentiation and integration
Numerical quadrature
Oscillatory functions
Physics
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Summary:The numerical evaluation of Hilbert transforms on the real line for functions that exhibit oscillatory behavior is investigated. A fairly robust numerical procedure is developed that is based on the use of convergence accelerator techniques. Several different types of oscillatory behavior are examined that can be successfully treated by the approach given. A few examples of functions whose oscillations are too extreme to deal with are also discussed.
ISSN:0010-4655
1879-2944
DOI:10.1016/S0010-4655(02)00155-8