The Solvability Complexity Index of Sampling-based Hilbert Transform Approximations

This paper determines the solvability complexity index (SCI) and a corresponding tower of algorithms for the computational problem of calculating the Hilbert transform of a continuous function with finite energy from its samples. It is shown that the SCI of these algorithms is equal to 2 and that the SCI is independent on whether the calculation is done by linear or by general (i.e. linear and/or non-linear) algorithms.