Hermite polynomials for signal reconstruction from zero-crossings. Part 1: one-dimensional signals

Generalised Hermite polynomials are employed for the reconstruction of an unknown signal from a knowledge of its zero-crossings, under certain conditions on its spatial/spectral width, but dispensing with the assumption of bandlimitedness. A computational implementation of the proposed method is given for one-variable (or one-dimensional) signals, featuring an application of simulated annealing for optimal reconstruction.