{"id":"https://openalex.org/W2157349623","doi":"https://doi.org/10.1109/lsp.2010.2045548","title":"Relationships Between $\\Psi _{ {\\tt B}}$-Energy Operator and Some Time-Frequency Representations","display_name":"Relationships Between $\\Psi _{ {\\tt B}}$-Energy Operator and Some Time-Frequency Representations","publication_year":2010,"publication_date":"2010-03-16","ids":{"openalex":"https://openalex.org/W2157349623","doi":"https://doi.org/10.1109/lsp.2010.2045548","mag":"2157349623"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2010.2045548","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2010.2045548","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01083621/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004893718","display_name":"Abdel\u2010Ouahab Boudraa","orcid":"https://orcid.org/0000-0002-1864-2859"},"institutions":[{"id":"https://openalex.org/I183158303","display_name":"\u00c9cole Navale","ror":"https://ror.org/030txnd05","country_code":"FR","type":"education","lineage":["https://openalex.org/I183158303"]},{"id":"https://openalex.org/I2801296886","display_name":"Institut de Recherche de l\u2019\u00c9cole Navale","ror":"https://ror.org/01v6shv96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I183158303","https://openalex.org/I190752583","https://openalex.org/I190861549","https://openalex.org/I2801296886","https://openalex.org/I4210134562"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Abdel-Ouahab Boudraa","raw_affiliation_strings":["IRENav, Ecole Navale, BCRM Brest, Brest, France","IRENAV - Institut de Recherche de l'Ecole Navale (F-29240 Brest - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRENav, Ecole Navale, BCRM Brest, Brest, France","institution_ids":["https://openalex.org/I183158303","https://openalex.org/I2801296886"]},{"raw_affiliation_string":"IRENAV - Institut de Recherche de l'Ecole Navale (F-29240 Brest - France)","institution_ids":["https://openalex.org/I183158303","https://openalex.org/I2801296886"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004893718"],"corresponding_institution_ids":["https://openalex.org/I183158303","https://openalex.org/I2801296886"],"apc_list":null,"apc_paid":null,"fwci":0.8242,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72331508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"17","issue":"6","first_page":"527","last_page":"530"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.996399998664856,"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":0.996399998664856,"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/T13493","display_name":"Optical and Acousto-Optic Technologies","score":0.9717000126838684,"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"}},{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9595000147819519,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/operator","display_name":"Operator (biology)","score":0.7007195949554443},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46319669485092163},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4603957533836365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37128400802612305}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.7007195949554443},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46319669485092163},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4603957533836365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37128400802612305},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/lsp.2010.2045548","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2010.2045548","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01083621v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01083621","pdf_url":"https://hal.science/hal-01083621/document","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Processing Letters, 2010, 17 (6), pp.527-530. &#x27E8;10.1109/LSP.2010.2045548&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:sam.ensam.eu:10985/8916","is_oa":true,"landing_page_url":"http://hdl.handle.net/10985/8916","pdf_url":"http://hdl.handle.net/10985/8916","source":{"id":"https://openalex.org/S4306400009","display_name":"SAM, the Arts et M\u00e9tiers ParisTech open access repository (Paris Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190752583","host_organization_name":"ParisTech","host_organization_lineage":["https://openalex.org/I190752583"],"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://hdl.handle.net/10985/8916","raw_type":null},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/77985","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/77985","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01083621v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01083621","pdf_url":"https://hal.science/hal-01083621/document","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Processing Letters, 2010, 17 (6), pp.527-530. &#x27E8;10.1109/LSP.2010.2045548&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2157349623.pdf","grobid_xml":"https://content.openalex.org/works/W2157349623.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1524521400","https://openalex.org/W1993705020","https://openalex.org/W1997623736","https://openalex.org/W2037315679","https://openalex.org/W2044545609","https://openalex.org/W2123133018","https://openalex.org/W2129377946","https://openalex.org/W2171902986","https://openalex.org/W2409556919","https://openalex.org/W6685400560"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"\u03a8":[0,23,32,55,81,103,131],"<sub":[1,24,33,56,82,104,132],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,25,34,57,83,105,133],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">B</sub>":[3,26,35,58,84,106,134],"operator":[4,8,27,36,59,85,107],"is":[5,67,86,115],"an":[6],"energy":[7],"that":[9,77],"measures":[10],"the":[11,89,93,100,122,138,141,145],"interactions":[12],"between":[13,31,54],"two":[14,61,71],"complex":[15],"signals.":[16,111],"In":[17],"this":[18],"letter,":[19],"new":[20],"properties":[21],"of":[22,60,80,92,102,126],"are":[28,51],"presented.":[29],"Connections":[30],"and":[37,48,64],"some":[38],"time-frequency":[39],"representations":[40],"(cross-ambiguity":[41],"function,":[42],"short-time":[43],"Fourier":[44,78],"transform,":[45,47],"Zak":[46],"Gabor":[49],"coefficients)":[50],"established.":[52],"Link":[53],"input":[62,73],"signals":[63],"their":[65],"cross-spectrum":[66],"also":[68],"derived.":[69],"For":[70],"equal":[72],"signals,":[74],"we":[75],"find":[76],"transform":[79],"proportional":[87],"to":[88,108,120,140],"second":[90,123],"derivative":[91],"ambiguity":[94],"function.":[95],"The":[96],"established":[97],"links":[98],"show":[99],"ability":[101],"analyze":[109],"nonstationary":[110],"A":[112],"numerical":[113],"example":[114],"provided":[116],"for":[117],"illustrating":[118],"how":[119],"estimate":[121],"order":[124],"moment,":[125],"a":[127],"FM":[128],"signal,":[129],"using":[130],"operator.":[135],"We":[136],"compare":[137],"result":[139],"moment":[142],"given":[143],"by":[144],"Wigner":[146],"Ville":[147],"distribution.":[148]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-18T10:00:31.954636","created_date":"2016-06-24T00:00:00"}
