I have to evaluate a Hilbert transform for some $\mathcal{L}^p(\mathbb{R},\mathbb{C})$-function ($1\leq p<\infty$). I know there are a number of algorithms out there to do it, but I don't have a full literature overview. I am aware of one of Stenger, which is based on Sinc approximation of analytic functions. But that is restricted to $p=1$ or $p=2$.
Short question: Any other favorable methods? Thanks for dropping some names and papers.
Best Answer
There is a very recent paper in Mathematics of Computation,
"Computing the Hilbert transform and its inverse"
Sheehan Olver
Math. Comp. 80 (2011), 1745-1767.
He presents a new algorithm and references some standard ones.
Good luck!
Tom