The integral transform obtained by defining ω congruent - tan(1/2 δ), and writing H(ω) = R(ω) + i X(ω), where R(ω) and X(ω) are a Hilbert transform pair as H(ω) = ρ(δ) - i χ(δ) (Papoulis 1962, p. 201).

Hilbert transform | integral transform