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Mathematics of Computation

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Computing the Hilbert transform on the real line

Author: J. A. C. Weideman
Journal: Math. Comp. 64 (1995), 745-762
MSC: Primary 65R10; Secondary 44A15, 65D30
MathSciNet review: 1277773
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Abstract: We introduce a new method for computing the Hilbert transform on the real line. It is a collocation method, based on an expansion in rational eigenfunctions of the Hilbert transform operator, and implemented through the Fast Fourier Transform. An error analysis is given, and convergence rates for some simple classes of functions are established. Numerical tests indicate that the method compares favorably with existing methods.

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Keywords: Hilbert transform, orthogonal rational eigenfunctions, Fast Fourier Transform
Article copyright: © Copyright 1995 American Mathematical Society