{"id":"https://openalex.org/W2001188743","doi":"https://doi.org/10.1109/tcsii.2012.2213363","title":"Phase Space Decomposition for Phase Noise and Synchronization Analysis of Planar Nonlinear Oscillators","display_name":"Phase Space Decomposition for Phase Noise and Synchronization Analysis of Planar Nonlinear Oscillators","publication_year":2012,"publication_date":"2012-09-19","ids":{"openalex":"https://openalex.org/W2001188743","doi":"https://doi.org/10.1109/tcsii.2012.2213363","mag":"2001188743"},"language":"en","primary_location":{"id":"doi:10.1109/tcsii.2012.2213363","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2012.2213363","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.04999","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053494231","display_name":"Michele Bonnin","orcid":"https://orcid.org/0000-0002-9106-563X"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Michele Bonnin","raw_affiliation_strings":["Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","Dept. of Electron. & Telecommun., Politec. di Torino, Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Dept. of Electron. & Telecommun., Politec. di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016472360","display_name":"Fernando Corinto","orcid":"https://orcid.org/0000-0003-4431-5701"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fernando Corinto","raw_affiliation_strings":["Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","Dept. of Electron. & Telecommun., Politec. di Torino, Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Dept. of Electron. & Telecommun., Politec. di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064241662","display_name":"Marco Gilli","orcid":"https://orcid.org/0000-0001-5765-4046"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Gilli","raw_affiliation_strings":["Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","Dept. of Electron. & Telecommun., Politec. di Torino, Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Dept. of Electron. & Telecommun., Politec. di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I177477856"],"apc_list":null,"apc_paid":null,"fwci":2.9463,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.91287037,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"59","issue":"10","first_page":"638","last_page":"642"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10187","display_name":"Radio Frequency Integrated Circuit Design","score":0.9998000264167786,"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/T10187","display_name":"Radio Frequency Integrated Circuit Design","score":0.9998000264167786,"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/T11417","display_name":"Advancements in PLL and VCO Technologies","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/T11449","display_name":"Mechanical and Optical Resonators","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6762247085571289},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6083489060401917},{"id":"https://openalex.org/keywords/phase-synchronization","display_name":"Phase synchronization","score":0.5547361969947815},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.49977684020996094},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4925402104854584},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.48827600479125977},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4760850965976715},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.45462915301322937},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.4380890130996704},{"id":"https://openalex.org/keywords/phase-noise","display_name":"Phase noise","score":0.423301100730896},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4000345766544342},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3929656744003296},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2970225214958191},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2910168766975403},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19419029355049133},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0847366452217102},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.0827665627002716},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.060359179973602295}],"concepts":[{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6762247085571289},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6083489060401917},{"id":"https://openalex.org/C194027367","wikidata":"https://www.wikidata.org/wiki/Q4420475","display_name":"Phase synchronization","level":3,"score":0.5547361969947815},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.49977684020996094},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4925402104854584},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.48827600479125977},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4760850965976715},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.45462915301322937},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4380890130996704},{"id":"https://openalex.org/C89631360","wikidata":"https://www.wikidata.org/wiki/Q1428766","display_name":"Phase noise","level":2,"score":0.423301100730896},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4000345766544342},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3929656744003296},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2970225214958191},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2910168766975403},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19419029355049133},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0847366452217102},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0827665627002716},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.060359179973602295},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tcsii.2012.2213363","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2012.2213363","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.04999","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.04999","pdf_url":"https://arxiv.org/pdf/1905.04999","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:porto.polito.it:2504238","is_oa":false,"landing_page_url":"http://porto.polito.it/2504238/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1549-7747","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1905.04999","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.04999","pdf_url":"https://arxiv.org/pdf/1905.04999","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1998943693","https://openalex.org/W2011842334","https://openalex.org/W2021023433","https://openalex.org/W2042623116","https://openalex.org/W2066120708","https://openalex.org/W2069493112","https://openalex.org/W2071861249","https://openalex.org/W2072558413","https://openalex.org/W2097007944","https://openalex.org/W2102337730","https://openalex.org/W2104340505","https://openalex.org/W2111079473","https://openalex.org/W2123684973","https://openalex.org/W2146140602","https://openalex.org/W2147863316","https://openalex.org/W2147942135","https://openalex.org/W2158906545"],"related_works":["https://openalex.org/W1963851439","https://openalex.org/W2095704199","https://openalex.org/W1827287738","https://openalex.org/W4210284618","https://openalex.org/W2114958893","https://openalex.org/W1995406459","https://openalex.org/W3033537072","https://openalex.org/W2068628444","https://openalex.org/W2022401564","https://openalex.org/W2082395593"],"abstract_inverted_index":{"Synchronization":[0],"phenomena,":[1],"frequency":[2],"shift,":[3],"and":[4,44,81],"phase":[5,45],"noise":[6,46],"are":[7],"often":[8],"limiting":[9],"key":[10],"factors":[11],"in":[12,78],"the":[13,24,37,57,60,64,73],"performances":[14],"of":[15,40,48,75],"oscillators.":[16,51],"The":[17],"perturbation":[18],"projection":[19,88],"method":[20],"allows":[21],"characterizing":[22],"how":[23],"oscillator's":[25],"output":[26],"is":[27,89],"modified":[28],"by":[29],"these":[30],"disturbances.":[31],"In":[32],"this":[33,76],"brief,":[34],"we":[35],"discuss":[36,72],"appropriate":[38],"decomposition":[39,77],"perturbations":[41,65],"for":[42,56],"synchronization":[43],"analysis":[47],"planar":[49],"nonlinear":[50],"We":[52,70],"derive":[53],"analytical":[54],"formulas":[55],"vectors":[58],"spanning":[59],"directions":[61],"along":[62],"which":[63],"have":[66],"to":[67,82],"be":[68],"projected.":[69],"also":[71],"implications":[74],"control":[79],"theory":[80],"what":[83],"extent":[84],"a":[85],"simple":[86],"orthogonal":[87],"correct.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}