Algorithm of adaptive Fourier decomposition in H2(ℂ+)

Abstract

In this paper, we propose an applicable algorithm of the so-called adaptive Fourier decomposition in [Formula: see text] the Hardy [Formula: see text] space on the upper half-plane [Formula: see text], which provides a new method for decomposing real-valued signals and analytic signals on the real line. As a by-product, a new approach for computing the Hilbert transform on the real line is also given. Numerical experiments are used to demonstrate the performance of the proposed algorithm.