{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T10:13:13Z","timestamp":1760955193278},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2010,3]]},"abstract":"<jats:p> This paper investigates how the mean envelope, the subtrahend in the sifting procedure for the Empirical Mode Decomposition (EMD) algorithm, represents as an expansion in terms of basis. To this end, a novel approach that gives an alternative analytical expression using B-spline functions is presented. The basic concept lies mainly on the idea that B-spline functions form a basis for the space of splines and have refined-node representations by knot insertion. This newly-developed expression is essentially equivalent to the conventional one, but gives a more explicit formulation on this issue. For the purpose of establishing the mathematical foundation of the EMD methodology, this study may afford a favorable opportunity in this direction. <\/jats:p>","DOI":"10.1142\/s0219691310003420","type":"journal-article","created":{"date-parts":[[2010,4,7]],"date-time":"2010-04-07T11:11:14Z","timestamp":1270638674000},"page":"175-195","source":"Crossref","is-referenced-by-count":3,"title":["B-SPLINE ANALYTICAL REPRESENTATION OF THE MEAN ENVELOPE FOR EMPIRICAL MODE DECOMPOSITION"],"prefix":"10.1142","volume":"08","author":[{"given":"TIANXIANG","family":"ZHENG","sequence":"first","affiliation":[{"name":"Shenzhen Tourism College, Jinan University, Shenzhen, Guangdong 518053, P. R. China"}]},{"given":"LIHUA","family":"YANG","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou, Guangdong 510275, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0193"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/9789812703347_0012"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S1793536909000096"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-004-7614-3"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691304000561"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2007.906771"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2007.901155"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691308002689"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691308002392"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2005.02.003"},{"key":"rf14","volume-title":"Methods of Spline Function","author":"Li Y. S.","year":"1979"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BF02916747"},{"key":"rf17","volume-title":"A Practical Guide to Splines","author":"de Boor C.","year":"2001"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691310003420","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:47:22Z","timestamp":1565200042000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691310003420"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3]]},"references-count":13,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2010,3]]}},"alternative-id":["10.1142\/S0219691310003420"],"URL":"https:\/\/doi.org\/10.1142\/s0219691310003420","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,3]]}}}