{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:30:33Z","timestamp":1726439433018},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv. Adapt. Data Anal."],"published-print":{"date-parts":[[2009,7]]},"abstract":"<jats:p> Motivated by the analytic signal approach and general construction methods by Qian et al. (accepted by Adv. Comput. Math.), we construct a class of orthonormal bases for the real signal space [Formula: see text], which have nonconstant physically meaningful instantaneous frequencies. We develop a fast algorithm for computing the Hilbert\u2013Fourier expansion of a given function in terms of the orthonormal bases. Moreover, we study the approximation properties of the Hilbert\u2013Fourier expansion. A numerical example is presented to demonstrate an adaptive Fourier expansion based on an optimal selection of the parameter a in the orthonormal bases according to the approximation error. <\/jats:p>","DOI":"10.1142\/s1793536909000163","type":"journal-article","created":{"date-parts":[[2009,7,23]],"date-time":"2009-07-23T11:31:54Z","timestamp":1248348714000},"page":"373-405","source":"Crossref","is-referenced-by-count":9,"title":["FAST NONLINEAR FOURIER EXPANSIONS"],"prefix":"10.1142","volume":"01","author":[{"given":"RUI","family":"WANG","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Graduate University of the Chinese Academy of Sciences, Beijing 100190, P. R. China"}]},{"given":"YUESHENG","family":"XU","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA"},{"name":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China"}]},{"given":"HAIZHANG","family":"ZHANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-004-7614-3"},{"volume-title":"Time-Frequency Analysis: Theory and Applications","year":"1995","author":"Cohen L.","key":"rf2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0193"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-005-9006-8"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-05-08067-6"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1109\/78.558469"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1216\/jiea\/1181075323"},{"volume-title":"Theory of H p Spaces","year":"1970","author":"Duren P. L.","key":"rf10"},{"volume-title":"Bounded Analytic Functions","year":"1981","author":"Garnett J. B.","key":"rf11"},{"volume-title":"Real and Complex Analysis","year":"1987","author":"Rudin W.","key":"rf12"},{"volume-title":"An Introduction to Nonharmonic Fourier Series","year":"1980","author":"Young R. M.","key":"rf13"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-005-0603-z"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392815"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6208-4"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1201\/9781420049985"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1598-1"},{"volume-title":"Numerical Analysis","year":"1996","author":"Kincaid D.","key":"rf20"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-97146-4"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626340"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19961770115"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(92)90266-Z"}],"container-title":["Advances in Adaptive Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793536909000163","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:28:11Z","timestamp":1565123291000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793536909000163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7]]},"references-count":21,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,7]]}},"alternative-id":["10.1142\/S1793536909000163"],"URL":"https:\/\/doi.org\/10.1142\/s1793536909000163","relation":{},"ISSN":["1793-5369","1793-7175"],"issn-type":[{"type":"print","value":"1793-5369"},{"type":"electronic","value":"1793-7175"}],"subject":[],"published":{"date-parts":[[2009,7]]}}}