{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T05:37:56Z","timestamp":1771911476806,"version":"3.50.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv. Adapt. Data Anal."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p> The Hilbert\u2013Huang Transform (HHT) decomposes time series into intrinsic mode functions (IMF) in time-frequency domain. We show that time slices of IMFs equal time slices of Fourier series, where the instantaneous parameters of the IMF define the parameters amplitude and phase of the Fourier series. This leads to the formulation of the theorem that nonstationary convolution of an IMF with a general time domain response function translates into a multiplication of the IMF with the respective spectral domain response function which is explicitly permitted to vary over time. We conclude and show on a real world application that a de-trended signal's IMFs can be convolved independently and then be used for further time-frequency analysis. Finally, a discussion is opened on parallels in HHT and the Fourier transform with respect to the time-frequency domain. <\/jats:p>","DOI":"10.1142\/s1793536913500040","type":"journal-article","created":{"date-parts":[[2013,4,23]],"date-time":"2013-04-23T21:29:15Z","timestamp":1366752555000},"page":"1350004","source":"Crossref","is-referenced-by-count":6,"title":["NONSTATIONARY TIME SERIES CONVOLUTION: ON THE RELATION BETWEEN THE HILBERT\u2013HUANG AND FOURIER TRANSFORM"],"prefix":"10.1142","volume":"05","author":[{"given":"MAIK","family":"NEUKIRCH","sequence":"first","affiliation":[{"name":"Barcelona Center for Subsurface Imaging, Institut de Ci\u00e8ncies del Mar, CSIC, Pg. Marit\u00edm de la Barceloneta 37-49, 08003 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"XAVIER","family":"GARCIA","sequence":"additional","affiliation":[{"name":"Barcelona Center for Subsurface Imaging, Institut de Ci\u00e8ncies del Mar, CSIC, Pg. Marit\u00edm de la Barceloneta 37-49, 08003 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,4,23]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2004.02203.x"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2012.05470.x"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015012821040"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1190\/1.2987375"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0193"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S1793536909000096"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1029\/2010GL043455"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/785243"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1190\/1.1444318"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0502"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1190\/1.1440255"}],"container-title":["Advances in Adaptive Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793536913500040","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:27:37Z","timestamp":1565170057000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793536913500040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":11,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2013,4,23]]},"published-print":{"date-parts":[[2013,1]]}},"alternative-id":["10.1142\/S1793536913500040"],"URL":"https:\/\/doi.org\/10.1142\/s1793536913500040","relation":{},"ISSN":["1793-5369","1793-7175"],"issn-type":[{"value":"1793-5369","type":"print"},{"value":"1793-7175","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}