{"id":"https://openalex.org/W1967719437","doi":"https://doi.org/10.1109/tit.1980.1056216","title":"Transient analysis of the second-order phase-locked loop in the presence of noise (Corresp.)","display_name":"Transient analysis of the second-order phase-locked loop in the presence of noise (Corresp.)","publication_year":1980,"publication_date":"1980-07-01","ids":{"openalex":"https://openalex.org/W1967719437","doi":"https://doi.org/10.1109/tit.1980.1056216","mag":"1967719437"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1980.1056216","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056216","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5112495821","display_name":"Ken\u2019ichi Nishiguchi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210133125","display_name":"Mitsubishi Electric (Japan)","ror":"https://ror.org/033y26782","country_code":"JP","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"K. Nishiguchi","raw_affiliation_strings":["Communication Equipment Works, Mitsubishi Electric Corporation Limited, Japan"],"affiliations":[{"raw_affiliation_string":"Communication Equipment Works, Mitsubishi Electric Corporation Limited, Japan","institution_ids":["https://openalex.org/I4210133125"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066223760","display_name":"Y. Uchida","orcid":null},"institutions":[{"id":"https://openalex.org/I4210133125","display_name":"Mitsubishi Electric (Japan)","ror":"https://ror.org/033y26782","country_code":"JP","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210133125"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Y. Uchida","raw_affiliation_strings":["Communication Equipment Works, Mitsubishi Electric Corporation Limited, Japan"],"affiliations":[{"raw_affiliation_string":"Communication Equipment Works, Mitsubishi Electric Corporation Limited, Japan","institution_ids":["https://openalex.org/I4210133125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112495821"],"corresponding_institution_ids":["https://openalex.org/I4210133125"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.10162527,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"4","first_page":"482","last_page":"486"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11417","display_name":"Advancements in PLL and VCO Technologies","score":0.9925000071525574,"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/T11417","display_name":"Advancements in PLL and VCO Technologies","score":0.9925000071525574,"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/T11236","display_name":"Control Systems and Identification","score":0.9778000116348267,"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/T11444","display_name":"Electromagnetic Compatibility and Noise Suppression","score":0.9736999869346619,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.7562930583953857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6032018661499023},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5686918497085571},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.5465086698532104},{"id":"https://openalex.org/keywords/phase-locked-loop","display_name":"Phase-locked loop","score":0.5419164896011353},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5272701382637024},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5143591165542603},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5115064382553101},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4845997095108032},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.48191311955451965},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.47114887833595276},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.4532455503940582},{"id":"https://openalex.org/keywords/characteristic-function","display_name":"Characteristic function (probability theory)","score":0.41979753971099854},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.394955039024353},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.3924878239631653},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36905455589294434},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2713974714279175},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10669669508934021},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10244214534759521},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09025001525878906},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08522862195968628}],"concepts":[{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.7562930583953857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6032018661499023},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5686918497085571},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.5465086698532104},{"id":"https://openalex.org/C12707504","wikidata":"https://www.wikidata.org/wiki/Q52637","display_name":"Phase-locked loop","level":3,"score":0.5419164896011353},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5272701382637024},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5143591165542603},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5115064382553101},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4845997095108032},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.48191311955451965},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.47114887833595276},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.4532455503940582},{"id":"https://openalex.org/C20538924","wikidata":"https://www.wikidata.org/wiki/Q822139","display_name":"Characteristic function (probability theory)","level":3,"score":0.41979753971099854},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.394955039024353},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3924878239631653},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36905455589294434},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2713974714279175},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10669669508934021},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10244214534759521},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09025001525878906},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08522862195968628},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1980.1056216","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056216","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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":7,"referenced_works":["https://openalex.org/W1572713988","https://openalex.org/W2005711636","https://openalex.org/W2012291463","https://openalex.org/W2111132411","https://openalex.org/W2135152728","https://openalex.org/W2148029592","https://openalex.org/W2159900489"],"related_works":["https://openalex.org/W1555216950","https://openalex.org/W2373670823","https://openalex.org/W2055750045","https://openalex.org/W2351359734","https://openalex.org/W1938615527","https://openalex.org/W1585046483","https://openalex.org/W2355760814","https://openalex.org/W1509341792","https://openalex.org/W2123188330","https://openalex.org/W2095860056"],"abstract_inverted_index":{"The":[0,25],"time-dependent":[1],"probability-density":[2],"function":[3,23],"(pdf)":[4],"of":[5,63,81,85],"the":[6,10,29,61,82],"state":[7],"vector":[8],"for":[9],"second-order":[11],"phase-locked":[12],"loop":[13],"(PLL)":[14],"is":[15,53],"shown":[16,55],"to":[17,31],"be":[18,47,75],"determined":[19],"by":[20,40,49,77],"an":[21],"orthogonal":[22],"expansion.":[24],"expansion":[26],"coefficients":[27],"are":[28,38],"solutions":[30,45],"infinite":[32],"dimensional":[33],"ordinary":[34],"differential":[35],"equations,":[36],"which":[37,59],"derived":[39],"Ito's":[41],"stochastic":[42],"calculus.":[43],"Numerical":[44],"can":[46,74],"obtained":[48],"truncating":[50],"them.":[51],"It":[52],"also":[54],"that":[56],"certain":[57],"parameters":[58],"characterize":[60],"distribution":[62],"a":[64,68],"random":[65],"variable":[66],"on":[67],"circle,":[69],"such":[70],"as":[71],"phase":[72],"error,":[73],"expressed":[76],"only":[78],"one":[79],"coefficient":[80],"Fourier":[83],"series":[84],"its":[86],"pdf.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}