{"id":"https://openalex.org/W2144555740","doi":"https://doi.org/10.1109/tsp.2009.2034939","title":"Performance of Instantaneous Frequency Rate Estimation Using High-Order Phase Function","display_name":"Performance of Instantaneous Frequency Rate Estimation Using High-Order Phase Function","publication_year":2009,"publication_date":"2009-10-22","ids":{"openalex":"https://openalex.org/W2144555740","doi":"https://doi.org/10.1109/tsp.2009.2034939","mag":"2144555740"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2009.2034939","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2034939","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","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/A5100383518","display_name":"Pu Wang","orcid":"https://orcid.org/0000-0002-4718-3102"},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pu Wang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ, USA","Dept. of Electr. & Comput. Eng., Stevens Inst. of Technol., Hoboken, NJ, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ, USA","institution_ids":["https://openalex.org/I108468826"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Stevens Inst. of Technol., Hoboken, NJ, USA#TAB#","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100365817","display_name":"Hongbin Li","orcid":"https://orcid.org/0000-0003-1453-847X"},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hongbin Li","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ, USA","Dept. of Electr. & Comput. Eng., Stevens Inst. of Technol., Hoboken, NJ, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ, USA","institution_ids":["https://openalex.org/I108468826"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Stevens Inst. of Technol., Hoboken, NJ, USA#TAB#","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011621698","display_name":"Igor Djurovi\u0107","orcid":"https://orcid.org/0000-0003-3856-2706"},"institutions":[{"id":"https://openalex.org/I5936373","display_name":"University of Montenegro","ror":"https://ror.org/02drrjp49","country_code":"ME","type":"education","lineage":["https://openalex.org/I5936373"]}],"countries":["ME"],"is_corresponding":false,"raw_author_name":"Igor Djurovic","raw_affiliation_strings":["Electrical Engineering Department, University of Montenegro, Podgorica, Montenegro","Electr. Eng. Dept., Univ. of Montenegro, Podgorica, Montenegro"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, University of Montenegro, Podgorica, Montenegro","institution_ids":["https://openalex.org/I5936373"]},{"raw_affiliation_string":"Electr. Eng. Dept., Univ. of Montenegro, Podgorica, Montenegro","institution_ids":["https://openalex.org/I5936373"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012490058","display_name":"Braham Himed","orcid":"https://orcid.org/0000-0003-0053-6270"},"institutions":[{"id":"https://openalex.org/I1280414376","display_name":"United States Air Force Research Laboratory","ror":"https://ror.org/02e2egq70","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280414376","https://openalex.org/I1330347796","https://openalex.org/I4210102105","https://openalex.org/I4389425425"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Braham Himed","raw_affiliation_strings":["AFRL/RYRT, Dayton, OH, USA","AFRL/RYRT, Dayton, OH USA"],"affiliations":[{"raw_affiliation_string":"AFRL/RYRT, Dayton, OH, USA","institution_ids":["https://openalex.org/I1280414376"]},{"raw_affiliation_string":"AFRL/RYRT, Dayton, OH USA","institution_ids":["https://openalex.org/I1280414376"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100383518"],"corresponding_institution_ids":["https://openalex.org/I108468826"],"apc_list":null,"apc_paid":null,"fwci":5.0976,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.9470438,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"4","first_page":"2415","last_page":"2421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11038","display_name":"Advanced SAR Imaging Techniques","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11038","display_name":"Advanced SAR Imaging Techniques","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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":0.9959999918937683,"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7908611297607422},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.6187707781791687},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6071050763130188},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.579587459564209},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5636899471282959},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5593236684799194},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.5426200032234192},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5051780343055725},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.46768811345100403},{"id":"https://openalex.org/keywords/delta-method","display_name":"Delta method","score":0.44837579131126404},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.4471903443336487},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.44430410861968994},{"id":"https://openalex.org/keywords/instantaneous-phase","display_name":"Instantaneous phase","score":0.43743035197257996},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3902057707309723},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3250812292098999},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3244047164916992},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28836455941200256},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21281984448432922},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.14398011565208435},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07749256491661072}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7908611297607422},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.6187707781791687},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6071050763130188},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.579587459564209},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5636899471282959},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5593236684799194},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5426200032234192},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5051780343055725},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.46768811345100403},{"id":"https://openalex.org/C971699","wikidata":"https://www.wikidata.org/wiki/Q1132714","display_name":"Delta method","level":3,"score":0.44837579131126404},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4471903443336487},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.44430410861968994},{"id":"https://openalex.org/C137798554","wikidata":"https://www.wikidata.org/wiki/Q6038852","display_name":"Instantaneous phase","level":3,"score":0.43743035197257996},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3902057707309723},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3250812292098999},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3244047164916992},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28836455941200256},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21281984448432922},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.14398011565208435},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07749256491661072},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2009.2034939","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2034939","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1588837646","https://openalex.org/W1596607002","https://openalex.org/W1963821050","https://openalex.org/W1966032405","https://openalex.org/W2010965358","https://openalex.org/W2039644648","https://openalex.org/W2058973663","https://openalex.org/W2072229229","https://openalex.org/W2103640336","https://openalex.org/W2121187169","https://openalex.org/W2139106846","https://openalex.org/W2145017037","https://openalex.org/W2154279661","https://openalex.org/W2161578447","https://openalex.org/W2169757381","https://openalex.org/W2170002490","https://openalex.org/W2170021087"],"related_works":["https://openalex.org/W2922895105","https://openalex.org/W1963866720","https://openalex.org/W4242644833","https://openalex.org/W2105938879","https://openalex.org/W2368727644","https://openalex.org/W2102148524","https://openalex.org/W2382484111","https://openalex.org/W2378802580","https://openalex.org/W2162273697","https://openalex.org/W1548785303"],"abstract_inverted_index":{"<para":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[2],"The":[3,54],"high-order":[4],"phase":[5,48],"function":[6],"(HPF)":[7],"is":[8],"a":[9,20,23],"useful":[10],"tool":[11],"to":[12,85],"estimate":[13,37],"the":[14,29,35,39,46,72,78],"instantaneous":[15],"frequency":[16],"rate":[17],"(IFR)":[18],"of":[19,34,77],"signal":[21,49],"with":[22,50,71],"polynomial":[24,47],"phase.":[25],"In":[26],"this":[27],"paper,":[28],"asymptotic":[30,65,73],"bias":[31],"and":[32,64,69],"variance":[33],"IFR":[36,59,80],"using":[38],"HPF":[40],"are":[41,67,83],"derived":[42],"in":[43,61],"closed-forms":[44],"for":[45,58],"an":[51],"arbitrary":[52],"order.":[53],"Cram\u00e9r-Rao":[55],"bounds":[56],"(CRBs)":[57],"estimation,":[60],"both":[62],"exact":[63],"forms,":[66],"obtained":[68],"compared":[70],"mean-square":[74],"error":[75],"(MSE)":[76],"HPF-based":[79],"estimator.":[81],"Simulations":[82],"provided":[84],"verify":[86],"our":[87],"theoretical":[88],"results.":[89],"</para>":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}