The Hilbert transform and inverse Hilbert transform are the integral transform
 |  | ![H[f(x)]=1/piPVint_(-infty)^infty(f(x)dx)/(x-y)](/images/equations/InverseHilbertTransform/Inline3.svg) |
(1)
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 |  | ![H^(-1)[g(y)]=-1/piPVint_(-infty)^infty(g(y)dy)/(y-x),](/images/equations/InverseHilbertTransform/Inline6.svg) |
(2)
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where the Cauchy principal value is taken in each of the integrals.
They will be implemented in a future version of the Wolfram Language as HilbertTransform[f, x, y] and InverseHilbertTransform[g, y, x], respectively.
