{"id":"https://openalex.org/W2888841903","doi":"https://doi.org/10.1109/ssp.2018.8450803","title":"Multidimensional Analytic Signal with Application on Graphs","display_name":"Multidimensional Analytic Signal with Application on Graphs","publication_year":2018,"publication_date":"2018-06-01","ids":{"openalex":"https://openalex.org/W2888841903","doi":"https://doi.org/10.1109/ssp.2018.8450803","mag":"2888841903"},"language":"en","primary_location":{"id":"doi:10.1109/ssp.2018.8450803","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssp.2018.8450803","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Statistical Signal Processing Workshop (SSP)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-01878753","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010482852","display_name":"Mikhail Tsitsvero","orcid":"https://orcid.org/0000-0002-3004-1036"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"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/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mikhail Tsitsvero","raw_affiliation_strings":["Univ Lyon, Inria, CNRS, ENS de Lyon, UCB Lyon 1, LIP UMR 5668, Lyon, France"],"affiliations":[{"raw_affiliation_string":"Univ Lyon, Inria, CNRS, ENS de Lyon, UCB Lyon 1, LIP UMR 5668, Lyon, France","institution_ids":["https://openalex.org/I4210144566","https://openalex.org/I100532134","https://openalex.org/I1326498283","https://openalex.org/I1294671590","https://openalex.org/I113428412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042411664","display_name":"Pierre Borgnat","orcid":"https://orcid.org/0000-0003-4536-8354"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Borgnat","raw_affiliation_strings":["Univ Lyon, ENS de Lyon, UCB Lyon 1, CNRS, Laboratoire de Physique, Lyon, France"],"affiliations":[{"raw_affiliation_string":"Univ Lyon, ENS de Lyon, UCB Lyon 1, CNRS, Laboratoire de Physique, Lyon, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101823619","display_name":"Paulo Gon\u00e7alv\u00e8s","orcid":"https://orcid.org/0000-0002-1781-6159"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"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/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Paulo Goncalves","raw_affiliation_strings":["Univ Lyon, Inria, CNRS, ENS de Lyon, UCB Lyon 1, LIP UMR 5668, Lyon, France"],"affiliations":[{"raw_affiliation_string":"Univ Lyon, Inria, CNRS, ENS de Lyon, UCB Lyon 1, LIP UMR 5668, Lyon, France","institution_ids":["https://openalex.org/I4210144566","https://openalex.org/I100532134","https://openalex.org/I1326498283","https://openalex.org/I1294671590","https://openalex.org/I113428412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010482852"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144566"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13034344,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"493","last_page":"497"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14438","display_name":"Advanced Scientific Research Methods","score":0.9520000219345093,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9347000122070312,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/hypercomplex-number","display_name":"Hypercomplex number","score":0.9292609691619873},{"id":"https://openalex.org/keywords/analytic-signal","display_name":"Analytic signal","score":0.7136878967285156},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6491058468818665},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.6245509386062622},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.48319995403289795},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48100385069847107},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47818973660469055},{"id":"https://openalex.org/keywords/multidimensional-signal-processing","display_name":"Multidimensional signal processing","score":0.4661869704723358},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.45448753237724304},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4256490468978882},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4147259294986725},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4101378321647644},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3015994429588318},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.3015068769454956},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2335052192211151},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.1981787085533142},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17023906111717224}],"concepts":[{"id":"https://openalex.org/C203249530","wikidata":"https://www.wikidata.org/wiki/Q837414","display_name":"Hypercomplex number","level":3,"score":0.9292609691619873},{"id":"https://openalex.org/C94727143","wikidata":"https://www.wikidata.org/wiki/Q485394","display_name":"Analytic signal","level":4,"score":0.7136878967285156},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6491058468818665},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.6245509386062622},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.48319995403289795},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48100385069847107},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47818973660469055},{"id":"https://openalex.org/C501101116","wikidata":"https://www.wikidata.org/wiki/Q18378116","display_name":"Multidimensional signal processing","level":4,"score":0.4661869704723358},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.45448753237724304},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4256490468978882},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4147259294986725},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4101378321647644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3015994429588318},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.3015068769454956},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2335052192211151},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.1981787085533142},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17023906111717224},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ssp.2018.8450803","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssp.2018.8450803","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Statistical Signal Processing Workshop (SSP)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01878753v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01878753","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":"SSP 2018 - IEEE Workshop on Statistical Signal Processing, IEEE, Jun 2018, Freiburg, Germany. pp.1-5","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01878753v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01878753","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":"SSP 2018 - IEEE Workshop on Statistical Signal Processing, IEEE, Jun 2018, Freiburg, Germany. pp.1-5","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W50138357","https://openalex.org/W93308513","https://openalex.org/W582756042","https://openalex.org/W1014650983","https://openalex.org/W1498385589","https://openalex.org/W1578099820","https://openalex.org/W1965274171","https://openalex.org/W1995601969","https://openalex.org/W2006554089","https://openalex.org/W2012076877","https://openalex.org/W2016410167","https://openalex.org/W2046630971","https://openalex.org/W2053186076","https://openalex.org/W2053683464","https://openalex.org/W2058558325","https://openalex.org/W2059917035","https://openalex.org/W2073995959","https://openalex.org/W2077269758","https://openalex.org/W2091791686","https://openalex.org/W2097854005","https://openalex.org/W2101491865","https://openalex.org/W2125963092","https://openalex.org/W2132518575","https://openalex.org/W2135269154","https://openalex.org/W2152816064","https://openalex.org/W2164760791","https://openalex.org/W2272460433","https://openalex.org/W2413238278","https://openalex.org/W2550731819","https://openalex.org/W2604921759","https://openalex.org/W2775908053","https://openalex.org/W2963166678","https://openalex.org/W2973818247","https://openalex.org/W3102635765","https://openalex.org/W3104995145","https://openalex.org/W4299552129"],"related_works":["https://openalex.org/W2916518000","https://openalex.org/W2916498667","https://openalex.org/W2917906954","https://openalex.org/W2572893131","https://openalex.org/W2917330019","https://openalex.org/W2917006597","https://openalex.org/W2916884673","https://openalex.org/W1897251165","https://openalex.org/W2423267406","https://openalex.org/W2097854005"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3,23,43],"provide":[4],"an":[5],"extension":[6],"to":[7,49],"analytic":[8,46],"signal":[9,47],"method":[10,48],"for":[11,16],"multidimensional":[12,45],"signals.":[13],"First,":[14],"expressions":[15],"separate":[17],"phase-shifted":[18,26],"components":[19,27],"are":[20],"given.":[21],"Second,":[22],"show":[24],"that":[25],"could":[28],"be":[29],"obtained":[30],"from":[31],"hypercomplex":[32,40],"Fourier":[33],"transform":[34],"in":[35],"the":[36],"algebra":[37],"of":[38],"commutative":[39],"numbers.":[41],"Finally":[42],"apply":[44],"signals":[50],"defined":[51],"on":[52],"graphs.":[53]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
