Sinc Approximation of Multidimensional Hilbert Transform and Its Applications

Many science and engineering applications require computing Hilbert transform. Sinc approximation is an efficient algorithm for computing one-dimensional (1D) Hilbert transform. In this paper, we develop Sinc approximation for computing multidimensional Hilbert transform and analyze its convergence rate. We apply our method to two applications: detecting edges of 2D images, and pricing discretely monitored barrier options and calculating survival probabilities in two-asset/three-asset models where the prices follow exponential Levy processes. Extensive numerical experiments confirm the efficiency of Sinc approximation for computing 2D and 3D Hilbert transforms in these applications.