Research PaperNo Access

Algorithm of adaptive Fourier decomposition in $H^{2} (ℂ^{+})$

Weixiong Mai

https://orcid.org/0000-0001-5361-125X

Macao Center for Mathematical Sciences, Macau University of Science and Technology, Macao, P. R. China

E-mail Address: wxmai@must.edu.mo

Corresponding author.

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and

Tao Qian

Macao Center for Mathematical Sciences, Macau University of Science and Technology, Macao, P. R. China

E-mail Address: tqian@must.edu.mo

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https://doi.org/10.1142/S021969132350011XCited by:0 (Source: Crossref)

Abstract

In this paper, we propose an applicable algorithm of the so-called adaptive Fourier decomposition in $H^{2} (ℂ^{+})$ the Hardy $H^{2}$ space on the upper half-plane $ℂ^{+}$ , 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.

Keywords:

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