{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T06:53:01Z","timestamp":1760597581770},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv. Adapt. Data Anal."],"published-print":{"date-parts":[[2013,7]]},"abstract":"<jats:p> It has been claimed that any expression of a(t) cos \u03b8(t) with a(t) as the instantaneous amplitude and cos \u03b8(t) as the carrier varying along with the phase \u03b8(t) could not be uniquely defined. However, based on the fact that a(t) cos \u03b8(t) with all its variational forms have the same numerical value at any given time, we propose the existence of a unique true intrinsic amplitude function a<jats:sub>i<\/jats:sub>(t) and phase function \u03b8<jats:sub>i<\/jats:sub>(t) that a<jats:sub>i<\/jats:sub>(t) cos \u03b8<jats:sub>i<\/jats:sub>(t) satisfying the envelope\u2013carrier relationship is the only expression making physical sense. A constructive method is also presented to find such amplitude-phase pair uniquely from any Intrinsic Mode Function (IMF). As a result, we can treat any IMF in the form of a<jats:sub>i<\/jats:sub>(t) cos \u03b8<jats:sub>i<\/jats:sub>(t) as the unique defined amplitude-phase pair, from which the instantaneous frequency (IF) can also be determined. <\/jats:p>","DOI":"10.1142\/s1793536913500118","type":"journal-article","created":{"date-parts":[[2013,8,29]],"date-time":"2013-08-29T00:29:08Z","timestamp":1377736148000},"page":"1350011","source":"Crossref","is-referenced-by-count":9,"title":["THE UNIQUENESS OF THE INSTANTANEOUS FREQUENCY BASED ON INTRINSIC MODE FUNCTION"],"prefix":"10.1142","volume":"05","author":[{"given":"NORDEN E.","family":"HUANG","sequence":"first","affiliation":[{"name":"Research Center for Adaptive Data Analysis, Center for Dynamical Biomarkers and Translational Medicine, National Central University, Zhongli, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VINCENT","family":"YOUNG","sequence":"additional","affiliation":[{"name":"Research Center for Adaptive Data Analysis, Center for Dynamical Biomarkers and Translational Medicine, National Central University, Zhongli, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MENTZUNG","family":"LO","sequence":"additional","affiliation":[{"name":"Research Center for Adaptive Data Analysis, Center for Dynamical Biomarkers and Translational Medicine, National Central University, Zhongli, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YUNG HUNG","family":"WANG","sequence":"additional","affiliation":[{"name":"Research Center for Adaptive Data Analysis, Center for Dynamical Biomarkers and Translational Medicine, National Central University, Zhongli, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C. K.","family":"PENG","sequence":"additional","affiliation":[{"name":"Research Center for Adaptive Data Analysis, Center for Dynamical Biomarkers and Translational Medicine, National Central University, Zhongli, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"XIANYAO","family":"CHEN","sequence":"additional","affiliation":[{"name":"First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong 266061, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GANG","family":"WANG","sequence":"additional","affiliation":[{"name":"First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong 266061, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIA","family":"DENG","sequence":"additional","affiliation":[{"name":"First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong 266061, P. R. 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