Robust multiscale analytic sampling approximation to periodic function and fast algorithm

Abstract

By applying the multiscale method to the Möbius transformation function, we construct the multiscale analytic sampling approximation (MASA) to any function in the Hardy space [Formula: see text]. The approximation error is estimated, and it is proved that the MASA is robust to sample error. We prove that the MASA can be expressed by a Hankel matrix, making use of which, a fast algorithm is established to compute the MASA. Since what we acquire in practice may well be the samples on time domain instead of the analytic ones on the unit disc of the complex plane, we establish a fast algorithm for acquiring analytic samples. Numerical experiments are carried out to demonstrate the efficiency of the MASA.