{"id":"https://openalex.org/W4396629581","doi":"https://doi.org/10.1109/lsp.2024.3396655","title":"Price's Theorem for Quaternion Variables","display_name":"Price's Theorem for Quaternion Variables","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4396629581","doi":"https://doi.org/10.1109/lsp.2024.3396655"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2024.3396655","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2024.3396655","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091932363","display_name":"Qiankun Diao","orcid":"https://orcid.org/0009-0000-6322-6312"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qiankun Diao","raw_affiliation_strings":["Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012826227","display_name":"Dongpo Xu","orcid":"https://orcid.org/0000-0002-9663-9743"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongpo Xu","raw_affiliation_strings":["Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044069210","display_name":"Shuning Sun","orcid":"https://orcid.org/0009-0002-1901-5942"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuning Sun","raw_affiliation_strings":["Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China","institution_ids":["https://openalex.org/I184983240"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103001848","display_name":"Danilo P. Mandic","orcid":"https://orcid.org/0000-0001-8432-3963"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Danilo P. Mandic","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5091932363"],"corresponding_institution_ids":["https://openalex.org/I184983240"],"apc_list":null,"apc_paid":null,"fwci":0.759,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71886937,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"31","issue":null,"first_page":"1424","last_page":"1428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.7929999828338623,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.7929999828338623,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.7354000210762024,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12504","display_name":"Mathematics and Applications","score":0.7070000171661377,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.7932721376419067},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46979889273643494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3998594880104065},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3574650287628174},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3453618288040161},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3374421000480652},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1197754442691803}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.7932721376419067},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46979889273643494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3998594880104065},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3574650287628174},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3453618288040161},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3374421000480652},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1197754442691803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2024.3396655","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2024.3396655","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7302374699","display_name":null,"funder_award_id":"62176051","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W28221659","https://openalex.org/W1855615675","https://openalex.org/W1921661266","https://openalex.org/W2009849827","https://openalex.org/W2036043111","https://openalex.org/W2065144261","https://openalex.org/W2067145564","https://openalex.org/W2090550497","https://openalex.org/W2094646141","https://openalex.org/W2108498575","https://openalex.org/W2114765937","https://openalex.org/W2116059849","https://openalex.org/W2116757668","https://openalex.org/W2118369318","https://openalex.org/W2124348301","https://openalex.org/W2161397505","https://openalex.org/W2169690868","https://openalex.org/W2331305061","https://openalex.org/W2803216379","https://openalex.org/W2955958653","https://openalex.org/W2978437779","https://openalex.org/W2990201147","https://openalex.org/W3092753424","https://openalex.org/W3127988379","https://openalex.org/W4226070437","https://openalex.org/W4313188585","https://openalex.org/W4385819848","https://openalex.org/W4388104002","https://openalex.org/W6678738811"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3127350447","https://openalex.org/W3108700312","https://openalex.org/W4225472102","https://openalex.org/W2382948573","https://openalex.org/W2887325221","https://openalex.org/W2084651007","https://openalex.org/W2184550115","https://openalex.org/W3121191907","https://openalex.org/W2391028436"],"abstract_inverted_index":{"Price's":[0,41,116,129],"theorem":[1,25,42,117,130],"in":[2,33,118],"statistical":[3,144],"signal":[4,120],"processing":[5,146],"relates":[6],"the":[7,47,58,76,90,93,101,112,140],"expectation":[8],"of":[9,13,61,71,78,95,128,142],"a":[10,23,96,125],"nonlinear":[11],"function":[12,97],"normally":[14],"distributed":[15],"random":[16,133],"variables":[17,45],"to":[18,28,64,75,88,100],"their":[19],"covariances.":[20],"However,":[21],"such":[22],"key":[24],"is":[26,53],"yet":[27],"be":[29],"established":[30],"and":[31,106,115],"explored":[32],"quaternion":[34,44,68,79,85,103,132,143],"statistics.":[35],"To":[36],"this":[37],"end,":[38],"we":[39,83,122],"introduce":[40],"for":[43,131],"using":[46],"generalized":[48],"Hamilton-real":[49],"(GHR)":[50],"calculus.":[51],"This":[52,135],"achieved":[54],"by":[55],"first":[56],"employing":[57],"chain":[59],"rule":[60],"GHR":[62],"calculus":[63],"derive":[65],"two":[66],"crucial":[67],"matrix":[69,80,105],"derivatives":[70],"functions":[72],"with":[73,98],"respect":[74,99],"product":[77],"variables.":[81,134],"Next,":[82],"leverage":[84],"second-order":[86],"statistics":[87],"establish":[89],"relationship":[91],"between":[92],"derivative":[94],"augmented":[102],"covariance":[104],"its":[107,150],"real":[108,119],"counterpart.":[109],"Based":[110],"on":[111],"above":[113],"results":[114],"processing,":[121],"finally":[123],"propose":[124],"novel":[126],"formulation":[127],"finding":[136],"not":[137],"only":[138],"enriches":[139],"theory":[141],"signals":[145],"but":[147],"also":[148],"extends":[149],"applicability.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
