{"id":"https://openalex.org/W2028497691","doi":"https://doi.org/10.1142/s1793536909000096","title":"ON INSTANTANEOUS FREQUENCY","display_name":"ON INSTANTANEOUS FREQUENCY","publication_year":2009,"publication_date":"2009-04-01","ids":{"openalex":"https://openalex.org/W2028497691","doi":"https://doi.org/10.1142/s1793536909000096","mag":"2028497691"},"language":"en","primary_location":{"id":"doi:10.1142/s1793536909000096","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793536909000096","pdf_url":null,"source":{"id":"https://openalex.org/S16439242","display_name":"Advances in Adaptive Data Analysis","issn_l":"1793-5369","issn":["1793-5369","1793-7175"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Adaptive Data Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110969892","display_name":"Norden E. Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I22265921","display_name":"National Central University","ror":"https://ror.org/00944ve71","country_code":"TW","type":"education","lineage":["https://openalex.org/I22265921"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"NORDEN E. HUANG","raw_affiliation_strings":["Research Center for Adaptive Data Analysis, National Central University, Chungli, Taiwan 32001, Republic of China"],"affiliations":[{"raw_affiliation_string":"Research Center for Adaptive Data Analysis, National Central University, Chungli, Taiwan 32001, Republic of China","institution_ids":["https://openalex.org/I22265921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087187626","display_name":"Zhaohua Wu","orcid":"https://orcid.org/0000-0003-1660-0724"},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ZHAOHUA WU","raw_affiliation_strings":["Department of Meteorology &amp; Center for Ocean-Atmospheric Prediction Studies, Florida State University, Tallahassee, FL 32306, USA"],"affiliations":[{"raw_affiliation_string":"Department of Meteorology &amp; Center for Ocean-Atmospheric Prediction Studies, Florida State University, Tallahassee, FL 32306, USA","institution_ids":["https://openalex.org/I103163165"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021398871","display_name":"Steven Long","orcid":"https://orcid.org/0000-0001-9629-4872"},"institutions":[{"id":"https://openalex.org/I1306266525","display_name":"Goddard Space Flight Center","ror":"https://ror.org/0171mag52","country_code":"US","type":"facility","lineage":["https://openalex.org/I1306266525","https://openalex.org/I4210124779"]},{"id":"https://openalex.org/I2802713533","display_name":"Wallops Flight Facility","ror":"https://ror.org/00r57r863","country_code":"US","type":"facility","lineage":["https://openalex.org/I2802713533","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"STEVEN R. LONG","raw_affiliation_strings":["NASA Goddard Space Flight Center, Ocean Sciences Branch/Code 614.2, Wallops Flight Facility, Wallops Island, VA 23337, USA"],"affiliations":[{"raw_affiliation_string":"NASA Goddard Space Flight Center, Ocean Sciences Branch/Code 614.2, Wallops Flight Facility, Wallops Island, VA 23337, USA","institution_ids":["https://openalex.org/I2802713533","https://openalex.org/I1306266525"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048229697","display_name":"Kenneth C. Arnold","orcid":"https://orcid.org/0000-0003-3892-9870"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"KENNETH C. ARNOLD","raw_affiliation_strings":["Department of Electric and Computer Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electric and Computer Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024291314","display_name":"Xianyao Chen","orcid":"https://orcid.org/0000-0001-9825-5295"},"institutions":[{"id":"https://openalex.org/I4210114556","display_name":"First Institute of Oceanography","ror":"https://ror.org/01y34t753","country_code":"CN","type":"facility","lineage":["https://openalex.org/I211433327","https://openalex.org/I4210114556","https://openalex.org/I4210127390"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XIANYAO CHEN","raw_affiliation_strings":["The First Institute of Oceanography, SOA, Qingdao 266061, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"The First Institute of Oceanography, SOA, Qingdao 266061, People's Republic of China","institution_ids":["https://openalex.org/I4210114556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112452855","display_name":"Karin Blank","orcid":null},"institutions":[{"id":"https://openalex.org/I1306266525","display_name":"Goddard Space Flight Center","ror":"https://ror.org/0171mag52","country_code":"US","type":"facility","lineage":["https://openalex.org/I1306266525","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"KARIN BLANK","raw_affiliation_strings":["Code 564, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA"],"affiliations":[{"raw_affiliation_string":"Code 564, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA","institution_ids":["https://openalex.org/I1306266525"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5110969892"],"corresponding_institution_ids":["https://openalex.org/I22265921"],"apc_list":null,"apc_paid":null,"fwci":70.8259,"has_fulltext":false,"cited_by_count":678,"citation_normalized_percentile":{"value":0.99969598,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"01","issue":"02","first_page":"177","last_page":"229"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10220","display_name":"Machine Fault Diagnosis Techniques","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10220","display_name":"Machine Fault Diagnosis Techniques","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/instantaneous-phase","display_name":"Instantaneous phase","score":0.8285460472106934},{"id":"https://openalex.org/keywords/hilbert-transform","display_name":"Hilbert transform","score":0.7699902057647705},{"id":"https://openalex.org/keywords/analytic-signal","display_name":"Analytic signal","score":0.7396134734153748},{"id":"https://openalex.org/keywords/hilbert-spectral-analysis","display_name":"Hilbert spectral analysis","score":0.6042819023132324},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.602010190486908},{"id":"https://openalex.org/keywords/hilbert\u2013huang-transform","display_name":"Hilbert\u2013Huang transform","score":0.5616428852081299},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.549595057964325},{"id":"https://openalex.org/keywords/time\u2013frequency-analysis","display_name":"Time\u2013frequency analysis","score":0.5036472678184509},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49551093578338623},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.478893905878067},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.4788486957550049},{"id":"https://openalex.org/keywords/energy-operator","display_name":"Energy operator","score":0.4659954309463501},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.4188840091228485},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4140487611293793},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.3682916760444641},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3427605926990509},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33792370557785034},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.21971362829208374},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21518832445144653},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.12280231714248657},{"id":"https://openalex.org/keywords/spectral-density","display_name":"Spectral density","score":0.08327823877334595}],"concepts":[{"id":"https://openalex.org/C137798554","wikidata":"https://www.wikidata.org/wiki/Q6038852","display_name":"Instantaneous phase","level":3,"score":0.8285460472106934},{"id":"https://openalex.org/C28799612","wikidata":"https://www.wikidata.org/wiki/Q685437","display_name":"Hilbert transform","level":3,"score":0.7699902057647705},{"id":"https://openalex.org/C94727143","wikidata":"https://www.wikidata.org/wiki/Q485394","display_name":"Analytic signal","level":4,"score":0.7396134734153748},{"id":"https://openalex.org/C207659853","wikidata":"https://www.wikidata.org/wiki/Q5761228","display_name":"Hilbert spectral analysis","level":4,"score":0.6042819023132324},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.602010190486908},{"id":"https://openalex.org/C25570617","wikidata":"https://www.wikidata.org/wiki/Q1006462","display_name":"Hilbert\u2013Huang transform","level":3,"score":0.5616428852081299},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.549595057964325},{"id":"https://openalex.org/C142433447","wikidata":"https://www.wikidata.org/wiki/Q7806653","display_name":"Time\u2013frequency analysis","level":3,"score":0.5036472678184509},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49551093578338623},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.478893905878067},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.4788486957550049},{"id":"https://openalex.org/C19579662","wikidata":"https://www.wikidata.org/wiki/Q461145","display_name":"Energy operator","level":3,"score":0.4659954309463501},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.4188840091228485},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4140487611293793},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3682916760444641},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3427605926990509},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33792370557785034},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.21971362829208374},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21518832445144653},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.12280231714248657},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.08327823877334595},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793536909000096","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793536909000096","pdf_url":null,"source":{"id":"https://openalex.org/S16439242","display_name":"Advances in Adaptive Data Analysis","issn_l":"1793-5369","issn":["1793-5369","1793-7175"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Adaptive Data Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8500000238418579}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W305332711","https://openalex.org/W1517729176","https://openalex.org/W1520309894","https://openalex.org/W1532679390","https://openalex.org/W1582484699","https://openalex.org/W1588381982","https://openalex.org/W1598517949","https://openalex.org/W1605417594","https://openalex.org/W1676457984","https://openalex.org/W1966425349","https://openalex.org/W1973048907","https://openalex.org/W1974086622","https://openalex.org/W1980039876","https://openalex.org/W1984918318","https://openalex.org/W1986788497","https://openalex.org/W1991946919","https://openalex.org/W2007221293","https://openalex.org/W2014412042","https://openalex.org/W2015544881","https://openalex.org/W2018897852","https://openalex.org/W2026117466","https://openalex.org/W2034226081","https://openalex.org/W2040532319","https://openalex.org/W2062024414","https://openalex.org/W2062233951","https://openalex.org/W2063643121","https://openalex.org/W2070912015","https://openalex.org/W2072202966","https://openalex.org/W2075627074","https://openalex.org/W2083407651","https://openalex.org/W2090218979","https://openalex.org/W2092409600","https://openalex.org/W2098395403","https://openalex.org/W2103436585","https://openalex.org/W2106665847","https://openalex.org/W2114509411","https://openalex.org/W2114537326","https://openalex.org/W2120390927","https://openalex.org/W2122470043","https://openalex.org/W2132085292","https://openalex.org/W2138402108","https://openalex.org/W2141802348","https://openalex.org/W2143593397","https://openalex.org/W2144678008","https://openalex.org/W2157000920","https://openalex.org/W2160097539","https://openalex.org/W2160724632","https://openalex.org/W2163785596","https://openalex.org/W2164651587","https://openalex.org/W2164847051","https://openalex.org/W2169791062","https://openalex.org/W2171483876","https://openalex.org/W2188563164","https://openalex.org/W2573780072","https://openalex.org/W2973818247","https://openalex.org/W3136463145","https://openalex.org/W3151807103","https://openalex.org/W4255272544","https://openalex.org/W4298352105","https://openalex.org/W4299552129"],"related_works":["https://openalex.org/W2166741655","https://openalex.org/W2393765384","https://openalex.org/W2510692285","https://openalex.org/W2028497691","https://openalex.org/W2349652637","https://openalex.org/W2364678610","https://openalex.org/W2075420061","https://openalex.org/W2069096863","https://openalex.org/W1605622899","https://openalex.org/W3159569091"],"abstract_inverted_index":{"Instantaneous":[0],"frequency":[1,161],"(IF)":[2],"is":[3,53,72,135,140,150,190],"necessary":[4],"for":[5,10,47],"understanding":[6],"the":[7,24,33,45,56,75,84,88,104,109,121,127,132,136,147,151,159,176,180],"detailed":[8],"mechanisms":[9],"nonlinear":[11],"and":[12,39,108,123,154,185],"nonstationary":[13],"processes.":[14],"Historically,":[15],"IF":[16,181],"was":[17],"computed":[18],"from":[19,144],"analytic":[20],"signal":[21],"(AS)":[22],"through":[23],"Hilbert":[25,77,85],"transform.":[26],"This":[27],"paper":[28],"offers":[29],"an":[30],"overview":[31],"of":[32,65,82,166,175],"difficulties":[34,46],"involved":[35],"in":[36],"using":[37],"AS,":[38],"two":[40],"new":[41],"methods":[42,99],"to":[43,54,87,100,142,158],"overcome":[44],"computing":[48],"IF.":[49],"The":[50,69],"first":[51],"approach":[52,71],"compute":[55,101],"quadrature":[57,125],"(defined":[58],"here":[59],"as":[60,74],"a":[61,163,186],"simple":[62],"90\u00b0":[63],"shift":[64],"phase":[66],"angle)":[67],"directly.":[68],"second":[70],"designated":[73],"normalized":[76],"transform":[78,86],"(NHT),":[79],"which":[80],"consists":[81],"applying":[83],"empirically":[89],"determined":[90],"FM":[91],"signals.":[92],"Additionally,":[93],"we":[94,118,172],"have":[95],"also":[96],"introduced":[97],"alternative":[98],"local":[102],"frequency,":[103],"generalized":[105],"zero-crossing":[106],"(GZC),":[107],"teager":[110],"energy":[111],"operator":[112],"(TEO)":[113],"methods.":[114],"Through":[115],"careful":[116],"comparisons,":[117],"found":[119],"that":[120],"NHT":[122],"direct":[124],"gave":[126],"best":[128],"overall":[129],"performance.":[130],"While":[131],"TEO":[133],"method":[134,149],"most":[137,152,174],"localized,":[138],"it":[139],"limited":[141,157],"data":[143],"linear":[145],"processes,":[146],"GZC":[148],"robust":[153],"accurate":[155],"although":[156],"mean":[160],"over":[162],"quarter":[164],"wavelength":[165],"temporal":[167],"resolution.":[168],"With":[169],"these":[170],"results,":[171],"believe":[173],"problems":[177],"associated":[178],"with":[179],"determination":[182],"are":[183],"resolved,":[184],"true":[187],"time\u2013frequency":[188],"analysis":[189],"thus":[191],"taking":[192],"another":[193],"step":[194],"toward":[195],"maturity.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":26},{"year":2024,"cited_by_count":34},{"year":2023,"cited_by_count":49},{"year":2022,"cited_by_count":50},{"year":2021,"cited_by_count":57},{"year":2020,"cited_by_count":46},{"year":2019,"cited_by_count":31},{"year":2018,"cited_by_count":48},{"year":2017,"cited_by_count":43},{"year":2016,"cited_by_count":52},{"year":2015,"cited_by_count":39},{"year":2014,"cited_by_count":46},{"year":2013,"cited_by_count":53},{"year":2012,"cited_by_count":37}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
