[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":10},"actionData","errors","root",{"_260":261},"routes/_layout",{"_11":180},"routes/entity.$type.$id",{"_11":12,"_13":14,"_15":16,"_17":18,"_19":20,"_21":22,"_23":24,"_25":26,"_27":28},"dehydratedState",{"_73":74,"_75":76},"type","paper","id","paper_W2142485381","section","technologies","entity",{"_15":16,"_29":30,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":38,"_39":-5,"_40":41,"_42":43,"_44":45,"_46":47,"_48":-5,"_49":50,"_51":30,"_52":53,"_54":55,"_56":57,"_58":59,"_60":61,"_62":-5,"_63":64,"_65":-5,"_66":67,"_68":30,"_69":-5},"canonical","https://www.hugmap.com/entity/paper/paper_W2142485381/technologies","siteBaseUrl","https://www.hugmap.com","sectionCount",2,"jsonLd","{\"@context\":\"https://schema.org\",\"@graph\":[{\"name\":\"A representation theorem and its applications to spherically-invariant random processes\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2142485381/technologies\",\"@type\":\"ScholarlyArticle\",\"headline\":\"A representation theorem and its applications to spherically-invariant random processes\",\"datePublished\":\"1973-09-01\",\"isPartOf\":{\"@type\":\"Periodical\",\"name\":\"IEEE Transactions on Information Theory\"}},{\"@type\":\"CollectionPage\",\"name\":\"A representation theorem and its applications to spherically-invariant random processes 相关技术\",\"description\":\"A representation theorem and its applications to spherically-invariant random processes 在 HugMap 中的相关技术，共 2 条，含结构化关联信息与详情链接。\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2142485381/technologies\",\"inLanguage\":\"zh-CN\"},{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"首页\",\"item\":\"https://www.hugmap.com/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"论文\",\"item\":\"https://www.hugmap.com/search?type=paper\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"A representation theorem and its applications to spherically-invariant random processes\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2142485381\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"相关技术\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2142485381/technologies\"}]}]}","name","A representation theorem and its applications to spherically-invariant random processes","nameZh","aliases","description","descriptionZh","status","active","externalIds","{\"openalex\":\"W2142485381\",\"doi\":\"10.1109/tit.1973.1055076\"}","properties","source","openalex","createdAt","2026-05-21T00:41:43.358604729","updatedAt","2026-05-21T00:41:43.358719248","doi","10.1109/tit.1973.1055076","arxivId","openalexId","W2142485381","title","abstractText","The n th-order characteristic functions (cf) of spherically-invariant random processes (sirp) with zero means are defined as cf, which are functions of n th-order quadratic forms of arbitrary positive definite matrices p . Every n th-order spherically-invariant characteristic function (sicf) is represented as a weighted Lebesgue-Stieltjes integral transform of an arbitrary univariate probability distribution function F(\\cdot) on [0,\\infty) . Furthermore, every n th-order sicf has a corresponding spherically-invariant probability density (sipd). Then we show that every n th-order sicf (or sipd) is a random mixture of a n th-order Gaussian cf [or probability density]. The randomization is performed on \\nu^2 \\rho , where \\nu is a random variable (tv) specified by the F(\\cdot) function. Examples of sirp are given. Relations to previously known results are discussed. Various expectation properties of Gaussian random processes are valid for sirp. Related conditional expectation, mean-square estimation, semMndependence, martingale, and closure properties are given. Finally, the form of the unit threshold likelihood ratio receiver in the detection of a known deterministic signal in additive sirp noise is shown to be a correlation receiver or a matched filter. The associated false-alarm and detection probabilities are expressed in closed forms.","publishedDate","1973-09-01","publishedYear",1973,"venue","IEEE Transactions on Information Theory","citationCount",309,"authors","keywords",[70,71,72],"pdfUrl","topVenue",false,"displayName","displayDescription","Random Matrices and Applications","Bayesian Methods and Mixture Models","Advanced Statistical Methods and Models","mutations",[],"queries",[77],{"_78":79,"_80":81,"_82":83,"_84":85},"dehydratedAt",1781601211075,"state",{"_87":88,"_89":90,"_91":79,"_92":-5,"_93":94,"_95":94,"_96":94,"_97":-5,"_98":-5,"_99":67,"_35":100,"_101":102},"queryKey",[86,19,14,16],"queryHash","[\"portal\",\"entity\",\"paper\",\"paper_W2142485381\"]","portal","data",{"_19":20,"_103":104,"_105":106,"_107":108,"_109":110,"_18":111,"_62":112},"dataUpdateCount",1,"dataUpdatedAt","error","errorUpdateCount",0,"errorUpdatedAt","fetchFailureCount","fetchFailureReason","fetchMeta","isInvalidated","success","fetchStatus","idle","entityType","Paper","taxonomies",[148,149,150],"events",[],"articles",[],[128,129],[113],{"_15":114,"_29":115,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":116,"_39":-5,"_40":41,"_42":117,"_44":118,"_119":-5,"_51":-5,"_120":-5,"_121":-5,"_122":-5,"_60":-5,"_123":-5,"_124":-5,"_125":-5,"_126":-5,"_127":-5,"_68":115,"_69":-5},"person_A5108338875","Kung Yao","{\"openalex\":\"A5108338875\"}","2026-05-20T21:56:10.179468841","2026-05-21T00:41:43.363865503","orcid","affiliation","researchArea","paperCount","homepage","linkedin","twitter","github","hindex",{"_15":144,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":145,"_39":-5,"_40":132,"_42":146,"_44":147,"_135":136,"_137":138,"_139":-5,"_140":141,"_142":-5,"_122":-5,"_143":-5,"_68":71,"_69":-5},{"_15":130,"_29":72,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":131,"_39":-5,"_40":132,"_42":133,"_44":134,"_135":136,"_137":138,"_139":-5,"_140":141,"_142":-5,"_122":-5,"_143":-5,"_68":72,"_69":-5},"tech_oa_T11871","{\"taxonomy_id\":\"tax_rd_T11871\"}","openalex_topics","2026-05-17T09:00:06.33811988","2026-05-17T09:00:06.338122501","techType","algorithm","domain","Physical Sciences","proposedYear","maturityLevel","growing","wikipediaUrl","patentCount","tech_oa_T11901","{\"taxonomy_id\":\"tax_rd_T11901\"}","2026-05-17T09:00:06.299899384","2026-05-17T09:00:06.299901847",{"_15":174,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":175,"_39":-5,"_40":41,"_42":176,"_44":177,"_155":156,"_157":-5,"_158":159,"_160":178,"_162":179,"_164":94,"_165":166,"_167":94,"_168":-5,"_68":71,"_69":-5},{"_15":169,"_29":72,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":170,"_39":-5,"_40":41,"_42":171,"_44":172,"_155":156,"_157":-5,"_158":159,"_160":161,"_162":173,"_164":94,"_165":166,"_167":94,"_168":-5,"_68":72,"_69":-5},{"_15":151,"_29":70,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":152,"_39":-5,"_40":41,"_42":153,"_44":154,"_155":156,"_157":-5,"_158":159,"_160":161,"_162":163,"_164":94,"_165":166,"_167":94,"_168":-5,"_68":70,"_69":-5},"tax_rd_T11716","{\"openalex_topic\":\"T11716\"}","2026-05-14T02:01:27.254620668","2026-05-23T10:29:20.234141864","taxonomyType","RESEARCH_DOMAIN","code","level",3,"parentId","tax_rd_2613","path","Physical Sciences/Mathematics/Statistics and Probability/Random Matrices and Applications","sortOrder","isLeaf",true,"entityCount","children","tax_rd_T11871","{\"openalex_topic\":\"T11871\"}","2026-05-14T00:28:04.221396823","2026-05-23T12:27:17.188104637","Physical Sciences/Mathematics/Statistics and Probability/Advanced Statistical Methods and Models","tax_rd_T11901","{\"openalex_topic\":\"T11901\"}","2026-05-14T00:28:03.432120766","2026-05-23T12:23:29.308890916","tax_rd_1702","Physical Sciences/Computer Science/Artificial Intelligence/Bayesian Methods and Mixture Models",{"_73":181,"_75":182},[],[183],{"_78":184,"_80":185,"_82":186,"_84":187},1781601208455,{"_87":189,"_89":90,"_91":184,"_92":-5,"_93":94,"_95":94,"_96":94,"_97":-5,"_98":-5,"_99":67,"_35":100,"_101":102},[86,188],"[\"portal\",\"industries\"]","industries",[190,191,192,193,194,195,196,197,198,199,200,201],{"_15":253,"_29":254,"_31":-5,"_32":255,"_33":256,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":257,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":254,"_69":256},{"_15":249,"_29":250,"_31":-5,"_32":-5,"_33":251,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":252,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":250,"_69":251},{"_15":243,"_29":244,"_31":-5,"_32":245,"_33":246,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":247,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":244,"_69":246},{"_15":239,"_29":240,"_31":-5,"_32":-5,"_33":241,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":242,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":240,"_69":241},{"_15":235,"_29":236,"_31":-5,"_32":-5,"_33":237,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":238,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":236,"_69":237},{"_15":229,"_29":230,"_31":-5,"_32":231,"_33":232,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":233,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":230,"_69":232},{"_15":225,"_29":226,"_31":-5,"_32":-5,"_33":227,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":228,"_164":94,"_165":166,"_167":94,"_168":-5,"_68":226,"_69":227},{"_15":221,"_29":222,"_31":-5,"_32":-5,"_33":223,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":224,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":222,"_69":223},{"_15":217,"_29":218,"_31":-5,"_32":-5,"_33":219,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":220,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":218,"_69":219},{"_15":213,"_29":214,"_31":-5,"_32":-5,"_33":215,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":216,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":214,"_69":215},{"_15":209,"_29":210,"_31":-5,"_32":-5,"_33":211,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":212,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":210,"_69":211},{"_15":202,"_29":203,"_31":-5,"_32":-5,"_33":204,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":205,"_42":-5,"_44":-5,"_155":206,"_157":-5,"_158":90,"_160":207,"_162":208,"_164":94,"_165":67,"_167":94,"_168":-5,"_68":203,"_69":204},"tax_ind_smartphone","智能手机","Smartphone","manual","INDUSTRY","tax_ind_root","科技行业/智能手机","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算","tax_ind_blockchain","区块链",[234],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[248],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[258,259],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_262":24},"SITE_BASE_URL"]

A representation theorem and its applications to spherically-invariant random processes 论文

A representation theorem and its applications to spherically-invariant random processes · 相关技术

相关技术