{"id":"https://openalex.org/W2605870031","doi":"https://doi.org/10.1109/tsp.2017.2736494","title":"Spectral Analysis of Stationary Random Bivariate Signals","display_name":"Spectral Analysis of Stationary Random Bivariate Signals","publication_year":2017,"publication_date":"2017-08-07","ids":{"openalex":"https://openalex.org/W2605870031","doi":"https://doi.org/10.1109/tsp.2017.2736494","mag":"2605870031"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2017.2736494","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2017.2736494","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1703.06417","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065125139","display_name":"Julien Flamant","orcid":"https://orcid.org/0000-0001-9994-173X"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I4210115519","display_name":"Centre de Recherche en Informatique","ror":"https://ror.org/020cdve92","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210115519","https://openalex.org/I70768539"]},{"id":"https://openalex.org/I4387153239","display_name":"Centre de Recherche en Informatique, Signal et Automatique de Lille","ror":"https://ror.org/05vrs3189","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2279609970","https://openalex.org/I4387153239","https://openalex.org/I7454413"]},{"id":"https://openalex.org/I7454413","display_name":"\u00c9cole Centrale de Lille","ror":"https://ror.org/01x441g73","country_code":"FR","type":"education","lineage":["https://openalex.org/I7454413"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Julien Flamant","raw_affiliation_strings":["Univ. Lille, CNRS, Centrale Lille, UMR 9189 \u2013 CRIStAL \u2013 Centre de Recherche en Informatique Signal et Automatique de Lille, Lille, France","Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Lille, CNRS, Centrale Lille, UMR 9189 \u2013 CRIStAL \u2013 Centre de Recherche en Informatique Signal et Automatique de Lille, Lille, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2279609970","https://openalex.org/I4210115519","https://openalex.org/I4387153239","https://openalex.org/I7454413"]},{"raw_affiliation_string":"Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189","institution_ids":["https://openalex.org/I4210115519","https://openalex.org/I4387153239"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022373992","display_name":"Nicolas Le Bihan","orcid":"https://orcid.org/0000-0001-6175-6045"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2800493309","display_name":"Grain Inspection, Packers and Stockyards Administration","ror":"https://ror.org/056mcm922","country_code":"US","type":"government","lineage":["https://openalex.org/I1336096307","https://openalex.org/I2800493309"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Nicolas Le Bihan","raw_affiliation_strings":["Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, Grenoble, France","GIPSA - Communication Information and Complex Systems"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, Grenoble, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006"]},{"raw_affiliation_string":"GIPSA - Communication Information and Complex Systems","institution_ids":["https://openalex.org/I2800493309","https://openalex.org/I4210124956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088402344","display_name":"Pierre Chainais","orcid":"https://orcid.org/0000-0003-4377-7584"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I4210115519","display_name":"Centre de Recherche en Informatique","ror":"https://ror.org/020cdve92","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210115519","https://openalex.org/I70768539"]},{"id":"https://openalex.org/I4387153239","display_name":"Centre de Recherche en Informatique, Signal et Automatique de Lille","ror":"https://ror.org/05vrs3189","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2279609970","https://openalex.org/I4387153239","https://openalex.org/I7454413"]},{"id":"https://openalex.org/I7454413","display_name":"\u00c9cole Centrale de Lille","ror":"https://ror.org/01x441g73","country_code":"FR","type":"education","lineage":["https://openalex.org/I7454413"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Chainais","raw_affiliation_strings":["Univ. Lille, CNRS, Centrale Lille, UMR 9189 \u2013 CRIStAL \u2013 Centre de Recherche en Informatique Signal et Automatique de Lille, Lille, France","Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Lille, CNRS, Centrale Lille, UMR 9189 \u2013 CRIStAL \u2013 Centre de Recherche en Informatique Signal et Automatique de Lille, Lille, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2279609970","https://openalex.org/I4210115519","https://openalex.org/I4387153239","https://openalex.org/I7454413"]},{"raw_affiliation_string":"Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189","institution_ids":["https://openalex.org/I4210115519","https://openalex.org/I4387153239"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":9,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0667,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.82429036,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"65","issue":"23","first_page":"6135","last_page":"6145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11698","display_name":"Underwater Acoustics Research","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9710999727249146,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/autocovariance","display_name":"Autocovariance","score":0.7904175519943237},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.782873272895813},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7018545866012573},{"id":"https://openalex.org/keywords/spectral-density-estimation","display_name":"Spectral density estimation","score":0.607208788394928},{"id":"https://openalex.org/keywords/spectral-density","display_name":"Spectral density","score":0.4902835190296173},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.4100729823112488},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.39671051502227783},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.35910338163375854},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32408207654953003},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20307821035385132},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18939733505249023},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09599724411964417}],"concepts":[{"id":"https://openalex.org/C88271906","wikidata":"https://www.wikidata.org/wiki/Q786973","display_name":"Autocovariance","level":3,"score":0.7904175519943237},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.782873272895813},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7018545866012573},{"id":"https://openalex.org/C30049272","wikidata":"https://www.wikidata.org/wiki/Q6555326","display_name":"Spectral density estimation","level":3,"score":0.607208788394928},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.4902835190296173},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.4100729823112488},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.39671051502227783},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35910338163375854},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32408207654953003},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20307821035385132},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18939733505249023},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09599724411964417},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsp.2017.2736494","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2017.2736494","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"},{"id":"pmh:oai:arXiv.org:1703.06417","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1703.06417","pdf_url":"https://arxiv.org/pdf/1703.06417","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:HAL:hal-01655097v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01655097","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ieeexplore.ieee.org/document/8003393/","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:lilloa.univ-lille.fr:20.500.12210/23663","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12210/23663","pdf_url":null,"source":{"id":"https://openalex.org/S4306402203","display_name":"LillOA (Universit\u00e9 de Lille (University Of Lille))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210123514","host_organization_name":"Centre d'Etudes en Civilisations, Langues et Litt\u00e9ratures Etrang\u00e8res","host_organization_lineage":["https://openalex.org/I4210123514"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1703.06417","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1703.06417","pdf_url":"https://arxiv.org/pdf/1703.06417","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W81722178","https://openalex.org/W178039687","https://openalex.org/W244729084","https://openalex.org/W323085160","https://openalex.org/W634311682","https://openalex.org/W639989723","https://openalex.org/W1963699493","https://openalex.org/W1976727013","https://openalex.org/W1979554463","https://openalex.org/W1983791336","https://openalex.org/W1995601969","https://openalex.org/W1998437656","https://openalex.org/W2002714615","https://openalex.org/W2004605483","https://openalex.org/W2022165146","https://openalex.org/W2043729845","https://openalex.org/W2049197221","https://openalex.org/W2058087147","https://openalex.org/W2060807102","https://openalex.org/W2069222481","https://openalex.org/W2076900674","https://openalex.org/W2089436497","https://openalex.org/W2090267260","https://openalex.org/W2092714340","https://openalex.org/W2093527373","https://openalex.org/W2093676263","https://openalex.org/W2096844050","https://openalex.org/W2097854005","https://openalex.org/W2108724231","https://openalex.org/W2110210567","https://openalex.org/W2135521223","https://openalex.org/W2139996618","https://openalex.org/W2140971281","https://openalex.org/W2145258586","https://openalex.org/W2145365886","https://openalex.org/W2150657581","https://openalex.org/W2153771600","https://openalex.org/W2155722796","https://openalex.org/W2159071216","https://openalex.org/W2163899311","https://openalex.org/W2167208435","https://openalex.org/W2170457951","https://openalex.org/W2263224228","https://openalex.org/W2639071670","https://openalex.org/W2799461614","https://openalex.org/W2917878399","https://openalex.org/W2963297042","https://openalex.org/W2994988665","https://openalex.org/W4211251910","https://openalex.org/W4214684912","https://openalex.org/W4234600779","https://openalex.org/W4240178185","https://openalex.org/W4285719527","https://openalex.org/W4295156079"],"related_works":["https://openalex.org/W2031428112","https://openalex.org/W2064515180","https://openalex.org/W4251726294","https://openalex.org/W1993505442","https://openalex.org/W2564659261","https://openalex.org/W4294006382","https://openalex.org/W2181164662","https://openalex.org/W2186403646","https://openalex.org/W3014721535","https://openalex.org/W2481210175"],"abstract_inverted_index":{"A":[0,84],"novel":[1],"approach":[2,133],"toward":[3],"the":[4,17,35,56,65,88,114,129,132],"spectral":[5,43,62,72,89,106],"analysis":[6],"of":[7,45,58,80,87,91,98,117,131],"stationary":[8],"random":[9,46,93,119],"bivariate":[10,32,47,69,94,120],"signals":[11,48],"is":[12,103,109],"proposed.":[13],"Unlike":[14],"existing":[15],"approaches,":[16],"proposed":[18],"framework":[19],"exhibits":[20],"a":[21,41,59,118],"natural":[22,85],"link":[23],"between":[24],"well-defined":[25],"statistical":[26],"objects":[27],"and":[28,64,100,111],"physical":[29],"parameters":[30],"for":[31,68],"signals.":[33,70],"Using":[34],"quaternion":[36],"Fourier":[37],"transform,":[38],"we":[39,112],"introduce":[40,113],"quaternion-valued":[42,61],"representation":[44],"seen":[49],"as":[50],"complex-valued":[51],"sequences.":[52],"This":[53,71],"makes":[54],"possible":[55],"definition":[57],"scalar":[60],"density":[63,73,90,107],"corresponding":[66],"autocovariance":[67],"can":[74],"be":[75],"meaningfully":[76],"interpreted":[77],"in":[78,96],"terms":[79,97],"frequency-dependent":[81],"polarization":[82,115],"attributes.":[83],"decomposition":[86],"any":[92],"signal":[95],"unpolarized":[99],"polarized":[101],"components":[102],"introduced.":[104],"Nonparametric":[105],"estimation":[108],"investigated,":[110],"periodogram":[116],"signal.":[121],"Numerical":[122],"experiments":[123],"support":[124],"our":[125],"theoretical":[126],"analysis,":[127],"illustrating":[128],"relevance":[130],"on":[134],"synthetic":[135],"data.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}