A new algorithm for the reconstruction of bandlimited functions and their Hilbert transform

This paper presents a new algorithm which permits the reconstruction of a hand-limited function from samples taken at not necessarily regularly spaced intervals, and also the recovery of the Hilbert transform of the function. For example, this enables the reconstruction of the real or the imaginary part of the dielectric permeability by means of the Kramers-Kronig relations. Regardless of the given sampling values, the algorithm converges in L₂ as well as pointwise and even. In contrast to known solutions, the algorithm requires no computation of Fourier integrals. Only a system of linear equations has to be solved in each iteration step. The approximating functions are distinguished by minimal energy. The new algorithm also applies to two-dimensional functions