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# Computing the Hilbert transform and its inverse

@article{Olver2011ComputingTH, title={Computing the Hilbert transform and its inverse}, author={Sheehan Olver}, journal={Math. Comput.}, year={2011}, volume={80}, pages={1745-1767} }

- Published 2011 in Math. Comput.
DOI:10.1090/S0025-5718-2011-02418-X

We construct a new method for approximating Hilbert transforms and their inverse throughout the complex plane. Both problems can be formulated as Riemann–Hilbert problems via Plemelj’s lemma. Using this framework, we rederive existing approaches for computing Hilbert transforms over the real line and unit interval, with the added benefit that we can compute the Hilbert transform in the complex plane. We then demonstrate the power of this approach by generalizing to the half line. Combining two… CONTINUE READING