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Process."],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s021969132350011x","type":"journal-article","created":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T01:45:05Z","timestamp":1675993505000},"source":"Crossref","is-referenced-by-count":0,"title":["Algorithm of adaptive Fourier decomposition in H2(\u2102+)"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5361-125X","authenticated-orcid":false,"given":"Weixiong","family":"Mai","sequence":"first","affiliation":[{"name":"Macao Center for Mathematical Sciences, Macau University of Science and Technology, Macao, P. R. China"}]},{"given":"Tao","family":"Qian","sequence":"additional","affiliation":[{"name":"Macao Center for Mathematical Sciences, Macau University of Science and Technology, Macao, P. R. 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