{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:14:11Z","timestamp":1773148451838,"version":"3.50.1"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv. Adapt. Data Anal."],"published-print":{"date-parts":[[2012,4]]},"abstract":"<jats:p> This paper mainly focuses on discussing the following three suspensions about the intrinsic mode functions (IMFs): (1) Whether more sifting times lead better symmetry to the IMFs or not? (2) Whether the upper and lower envelopes of each IMF degenerate to a pair of symmetric straight lines as the sifting times tend to infinity or not? (3) Whether the average frequencies of the neighboring IMFs get closer enough as the sifting times tend to infinity or not? The first suspension has direct relation to the stoppage criteria, which is of critical importance in the successful implementation of empirical mode decomposition (EMD) method. The second suspension is actually a rigid theoretical result given by Wang et al. [2010], but it may be failed for the actual sifting. The third suspension is associated with the conjecture given by Wu and Huang [2010]. In addition, the frequency distribution problem is also on the way of the last suspension. By considering the variation of maximum amplitude for the mean curve, we find that, after a certain sifting times, the symmetry degree of the IMFs behaves in an intermittent manner. This asymptotic behavior indicates that the first suspension is false in all probability. Further investigation shows that the theoretical result given by Wang et al. [2010] is out of reach. It follows from the sifting tests that the frequency ratio for neighboring IMFs cannot decrease to 1 and the last suspension is cracked. Different from the common sense, there is a very interesting phenomenon that the extreme points of the first IMF may be more than that of the original data. The statistical results on a large quantity of field data show that the frequency distribution along the empirical modes roughly obeys an exponential law. In addition, a new mode-number formula is deduced, which is more reasonable than the one given by Wu and Huang [2009]. <\/jats:p>","DOI":"10.1142\/s1793536912500082","type":"journal-article","created":{"date-parts":[[2012,8,31]],"date-time":"2012-08-31T05:17:51Z","timestamp":1346390271000},"page":"1250008","source":"Crossref","is-referenced-by-count":4,"title":["WHAT ABOUT THE ASYMPTOTIC BEHAVIOR OF THE INTRINSIC MODE FUNCTIONS AS THE SIFTING TIMES TEND TO INFINITY?"],"prefix":"10.1142","volume":"04","author":[{"given":"JIN-LIANG","family":"WANG","sequence":"first","affiliation":[{"name":"College of Science, Qingdao Technological University, East Jialingjiang Road, No. 777, Huangdao Region of Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ZONG-JUN","family":"LI","sequence":"additional","affiliation":[{"name":"College of Science, Qingdao Technological University, East Jialingjiang Road, No. 777, Huangdao Region of Qingdao 266520, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,8,31]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2003.821662"},{"key":"rf2","first-page":"RG2006","volume":"46","author":"Huang N. E.","journal-title":"Rev. Geophys."},{"key":"rf3","first-page":"903C995","volume":"454","author":"Huang N. E.","journal-title":"Proc. R. Soc. Lond. A"},{"key":"rf4","first-page":"3217C2345","volume":"459","author":"Huang N. E.","journal-title":"Proc. R. Soc. Lond. A"},{"key":"rf6","first-page":"277C293","volume":"2","author":"Wang G.","journal-title":"Adv. Adap. Data Anal."},{"key":"rf7","first-page":"1C41","volume":"1","author":"Wu Z.","journal-title":"Adv. Adap. Data Analy."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S1793536910000604"}],"container-title":["Advances in Adaptive Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793536912500082","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T10:18:50Z","timestamp":1565173130000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793536912500082"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4]]},"references-count":7,"journal-issue":{"issue":"01n02","published-online":{"date-parts":[[2012,8,31]]},"published-print":{"date-parts":[[2012,4]]}},"alternative-id":["10.1142\/S1793536912500082"],"URL":"https:\/\/doi.org\/10.1142\/s1793536912500082","relation":{},"ISSN":["1793-5369","1793-7175"],"issn-type":[{"value":"1793-5369","type":"print"},{"value":"1793-7175","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4]]}}}