{"id":"https://openalex.org/W2100628929","doi":"https://doi.org/10.1109/tsp.2009.2021501","title":"An Exact Direct Method of Sinusoidal Parameter Estimation Derived From Finite Fourier Integral of Differential Equation","display_name":"An Exact Direct Method of Sinusoidal Parameter Estimation Derived From Finite Fourier Integral of Differential Equation","publication_year":2009,"publication_date":"2009-04-24","ids":{"openalex":"https://openalex.org/W2100628929","doi":"https://doi.org/10.1109/tsp.2009.2021501","mag":"2100628929"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2009.2021501","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2021501","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/A5057055015","display_name":"Shigeru Ando","orcid":"https://orcid.org/0000-0003-4618-5293"},"institutions":[{"id":"https://openalex.org/I14396692","display_name":"Tokyo University of Information Sciences","ror":"https://ror.org/044bdx604","country_code":"JP","type":"education","lineage":["https://openalex.org/I14396692"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"S. Ando","raw_affiliation_strings":["Department of Information Physics and Computing, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan","Dept. of Inf., Phys. & Comput., Univ. of Tokyo, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Physics and Computing, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I14396692","https://openalex.org/I74801974"]},{"raw_affiliation_string":"Dept. of Inf., Phys. & Comput., Univ. of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072749899","display_name":"Takaaki Nara","orcid":"https://orcid.org/0000-0002-9955-4542"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"T. Nara","raw_affiliation_strings":["Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications, Tokyo, Japan","Dept. of Mechanical Eng. & Intelligent Syst., University of Electro-Communications, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications, Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]},{"raw_affiliation_string":"Dept. of Mechanical Eng. & Intelligent Syst., University of Electro-Communications, Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.188,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.95624516,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"57","issue":"9","first_page":"3317","last_page":"3329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9997000098228455,"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/T10573","display_name":"Power Quality and Harmonics","score":0.9908999800682068,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/mathematics","display_name":"Mathematics","score":0.7624691128730774},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6367268562316895},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6046321392059326},{"id":"https://openalex.org/keywords/cram\u00e9r\u2013rao-bound","display_name":"Cram\u00e9r\u2013Rao bound","score":0.518302857875824},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4754497706890106},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4744128882884979},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4592449963092804},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.4467565715312958},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4296322166919708},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34478700160980225},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32605117559432983},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1378159523010254}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7624691128730774},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6367268562316895},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6046321392059326},{"id":"https://openalex.org/C4978587","wikidata":"https://www.wikidata.org/wiki/Q1138810","display_name":"Cram\u00e9r\u2013Rao bound","level":3,"score":0.518302857875824},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4754497706890106},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4744128882884979},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4592449963092804},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.4467565715312958},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4296322166919708},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34478700160980225},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32605117559432983},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1378159523010254}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2009.2021501","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2021501","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W1492553521","https://openalex.org/W1963864898","https://openalex.org/W1968214196","https://openalex.org/W1968798514","https://openalex.org/W1979696290","https://openalex.org/W1992475048","https://openalex.org/W1994275403","https://openalex.org/W1995130266","https://openalex.org/W1995713109","https://openalex.org/W1996348247","https://openalex.org/W2001188690","https://openalex.org/W2001729062","https://openalex.org/W2001762009","https://openalex.org/W2010492472","https://openalex.org/W2011270065","https://openalex.org/W2019833178","https://openalex.org/W2022542144","https://openalex.org/W2025934813","https://openalex.org/W2032097072","https://openalex.org/W2033332370","https://openalex.org/W2058207471","https://openalex.org/W2067718036","https://openalex.org/W2074086498","https://openalex.org/W2080655656","https://openalex.org/W2088460084","https://openalex.org/W2089213691","https://openalex.org/W2089957712","https://openalex.org/W2096990949","https://openalex.org/W2098540416","https://openalex.org/W2100567194","https://openalex.org/W2103820741","https://openalex.org/W2106908360","https://openalex.org/W2110973272","https://openalex.org/W2111855076","https://openalex.org/W2114166389","https://openalex.org/W2114763873","https://openalex.org/W2115128368","https://openalex.org/W2117457712","https://openalex.org/W2121495791","https://openalex.org/W2124268221","https://openalex.org/W2127451329","https://openalex.org/W2138680881","https://openalex.org/W2139150818","https://openalex.org/W2141820190","https://openalex.org/W2147367660","https://openalex.org/W2148723353","https://openalex.org/W2149460029","https://openalex.org/W2152280136","https://openalex.org/W2153203408","https://openalex.org/W2164739738","https://openalex.org/W2165887549","https://openalex.org/W2166764037","https://openalex.org/W2170211487","https://openalex.org/W3137136951","https://openalex.org/W4292156489","https://openalex.org/W6629558999"],"related_works":["https://openalex.org/W1479746946","https://openalex.org/W2055757274","https://openalex.org/W2511739151","https://openalex.org/W2143803213","https://openalex.org/W2155014562","https://openalex.org/W2134404114","https://openalex.org/W1964936841","https://openalex.org/W2026659681","https://openalex.org/W2185708237","https://openalex.org/W2094657987"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,23,43,71],"propose":[4],"a":[5,31,60],"novel":[6],"method":[7],"for":[8,41,99,117,129],"estimating":[9],"the":[10,21,26,49,56,94,109,120,126,131,141,165],"parameters":[11],"(frequency,":[12],"amplitude,":[13],"and":[14,36,93,125,157,167],"phase)":[15],"of":[16,30,48,63],"real":[17],"sinusoids.":[18],"To":[19,33],"derive":[20],"estimator,":[22],"start":[24],"from":[25,144],"characteristic":[27],"differential":[28,50,57],"equation":[29,58],"sinusoid.":[32],"remove":[34],"differentials":[35],"obtain":[37],"an":[38,148],"algebraic":[39],"relation":[40,95],"frequency,":[42],"introduce":[44],"finite-period":[45],"weighted":[46,142],"integrals":[47,143],"equation,":[51],"which":[52],"become":[53],"equivalent":[54],"to":[55,81,119,139],"when":[59],"sufficient":[61],"number":[62],"weight":[64,69],"functions":[65],"are":[66,84,88,104,137,153,162],"applied.":[67],"As":[68],"functions,":[70],"show":[72],"that":[73],"Fourier":[74,91,170],"kernels":[75],"have":[76],"excellent":[77],"properties.":[78],"Terms":[79],"related":[80],"integral":[82],"boundaries":[83],"readily":[85],"eliminated,":[86],"observations":[87],"provided":[89],"by":[90],"coefficients,":[92],"becomes":[96],"independently":[97],"accurate":[98],"multiple":[100],"sinusoids":[101],"if":[102],"they":[103],"sufficiently":[105],"spaced.":[106],"We":[107],"solve":[108],"obtained":[110],"equations":[111],"in":[112],"two":[113],"ways:":[114],"one":[115],"is":[116,128],"approaching":[118],"Cramer-Rao":[121],"lower":[122],"bound":[123],"(CRLB),":[124],"other":[127,168],"enhancing":[130],"interference":[132],"rejection":[133],"capability.":[134],"Also,":[135],"methods":[136],"proposed":[138],"calculate":[140],"sampled":[145],"signals":[146],"with":[147,164],"improved":[149],"accuracy.":[150],"Proposed":[151],"algorithms":[152],"examined":[154],"under":[155],"noise":[156],"sinusoidal":[158],"interference.":[159],"Error":[160],"variances":[161],"compared":[163],"CRLB":[166],"fast":[169],"transform":[171],"(FFT)-based":[172],"methods.":[173]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}