{"id":"https://openalex.org/W2940937097","doi":"https://doi.org/10.1109/tim.2019.2906333","title":"On Bussgang\u2019s Theorem, Separability, and Colored Random Phase Multisines","display_name":"On Bussgang\u2019s Theorem, Separability, and Colored Random Phase Multisines","publication_year":2019,"publication_date":"2019-04-25","ids":{"openalex":"https://openalex.org/W2940937097","doi":"https://doi.org/10.1109/tim.2019.2906333","mag":"2940937097"},"language":"en","primary_location":{"id":"doi:10.1109/tim.2019.2906333","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2019.2906333","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","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/A5067784521","display_name":"Tadeusz Dobrowiecki","orcid":"https://orcid.org/0000-0002-8307-5096"},"institutions":[{"id":"https://openalex.org/I29770179","display_name":"Budapest University of Technology and Economics","ror":"https://ror.org/02w42ss30","country_code":"HU","type":"education","lineage":["https://openalex.org/I29770179"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Tadeusz P. Dobrowiecki","raw_affiliation_strings":["Department of Measurement and Information Systems, Budapest University of Technology and Economics, Budapest, Hungary"],"raw_orcid":"https://orcid.org/0000-0002-8307-5096","affiliations":[{"raw_affiliation_string":"Department of Measurement and Information Systems, Budapest University of Technology and Economics, Budapest, Hungary","institution_ids":["https://openalex.org/I29770179"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067784521"],"corresponding_institution_ids":["https://openalex.org/I29770179"],"apc_list":null,"apc_paid":null,"fwci":0.6225,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70233207,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"69","issue":"3","first_page":"907","last_page":"915"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9955000281333923,"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/harmonics","display_name":"Harmonics","score":0.5783370137214661},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5616677403450012},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.5543182492256165},{"id":"https://openalex.org/keywords/colors-of-noise","display_name":"Colors of noise","score":0.5516180992126465},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.5293501019477844},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4861156940460205},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.48001614212989807},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.466388463973999},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.46627476811408997},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4365774691104889},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.42418208718299866},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.42402273416519165},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40424445271492004},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3589383363723755},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3462798297405243},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19933569431304932},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18392091989517212},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14806005358695984},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1017487645149231}],"concepts":[{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.5783370137214661},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5616677403450012},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.5543182492256165},{"id":"https://openalex.org/C114996537","wikidata":"https://www.wikidata.org/wiki/Q4854529","display_name":"Colors of noise","level":3,"score":0.5516180992126465},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.5293501019477844},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4861156940460205},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.48001614212989807},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.466388463973999},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.46627476811408997},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4365774691104889},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.42418208718299866},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.42402273416519165},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40424445271492004},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3589383363723755},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3462798297405243},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19933569431304932},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18392091989517212},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14806005358695984},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1017487645149231},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tim.2019.2906333","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2019.2906333","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"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 Instrumentation and Measurement","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.5899999737739563,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1483508733","https://openalex.org/W1494908267","https://openalex.org/W1501433466","https://openalex.org/W1515361063","https://openalex.org/W1630120088","https://openalex.org/W1988864101","https://openalex.org/W2002250726","https://openalex.org/W2072820189","https://openalex.org/W2106578181","https://openalex.org/W2115382461","https://openalex.org/W2119013895","https://openalex.org/W2124703077","https://openalex.org/W2137720674","https://openalex.org/W2140775419","https://openalex.org/W2144239679","https://openalex.org/W2153604954","https://openalex.org/W2334309179","https://openalex.org/W2407429584","https://openalex.org/W2795247000","https://openalex.org/W2982837428","https://openalex.org/W2986809256","https://openalex.org/W4252099851","https://openalex.org/W6628989521","https://openalex.org/W6629380985","https://openalex.org/W6629821884"],"related_works":["https://openalex.org/W2349980442","https://openalex.org/W1968911901","https://openalex.org/W2790395016","https://openalex.org/W1974392290","https://openalex.org/W3143465902","https://openalex.org/W3103566292","https://openalex.org/W2074565401","https://openalex.org/W1607924090","https://openalex.org/W1700578922","https://openalex.org/W2922917287"],"abstract_inverted_index":{"Random":[0,119],"phase":[1,114,120,157,219,241],"multisines":[2,74,115,121,158,220,242],"tend":[3],"asymptotically,":[4],"with":[5,54,122,209],"an":[6,27,174,236],"increasing":[7,210],"number":[8,69],"of":[9,13,39,58,70,95,137,182,191],"harmonics":[10],"and":[11,22,111,131,203,230],"irrespective":[12],"their":[14],"spectral":[15,125,201],"coloring,":[16,126],"to":[17,29,32,51,80,104,134,150,227,244],"the":[18,34,46,68,92,105,135,162,183,189,192,200],"Gaussian":[19,30,55,81,109,228],"amplitude":[20],"distribution":[21],"can":[23],"be":[24],"used":[25,160],"as":[26],"alternative":[28,226],"signals":[31,130],"measure":[33],"best":[35],"linear":[36],"approximation":[37,184],"(BLA)":[38],"nonlinear":[40],"systems.":[41],"The":[42],"asymptotic":[43],"error":[44,193],"on":[45,199],"measured":[47,53,93],"frequency":[48],"characteristics,":[49],"compared":[50],"that":[52,107,188,216],"noise,":[56,82],"is":[57,67,90,102,206],"order":[59,175],"O(M":[60,176],"<sup":[61,177],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[62,178],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-1</sup>":[63],"),":[64],"where":[65],"M":[66],"harmonics.":[71],"Flat":[72],"(white)":[73],"are":[75,116,128,159,221],"still":[76],"a":[77,86,96,123,138,145,196,223,232,248],"better":[78,233],"approximant":[79],"because":[83],"even":[84,231],"in":[85,161,195,214,247],"nonasymptotic":[87],"setting":[88],"(M":[89],"low),":[91],"BLA":[94,136],"static":[97,139],"nonlinearity":[98],"remains":[99],"static.":[100],"This":[101],"due":[103,243],"fact":[106],"both":[108],"noise":[110,229],"flat":[112,155,239],"random":[113,156,218,240],"separable":[117],"signals.":[118],"nonflat":[124],"however,":[127],"nonseparable":[129],"introduce":[132],"dynamics":[133,190],"nonlinearity,":[140],"which":[141],"was":[142],"observed":[143],"for":[144,235],"low":[146],"harmonic":[147],"number.":[148],"Due":[149],"this":[151,165,171,204],"reason,":[152],"usually,":[153],"only":[154],"applications.":[163],"In":[164],"paper,":[166],"we":[167],"investigate":[168],"more":[169,245],"deeply":[170],"phenomenon,":[172],"performing":[173],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-2</sup>":[179],")":[180],"analysis":[181],"error.":[185],"We":[186,212],"show":[187],"depend,":[194],"simple":[197],"way,":[198],"coloring":[202],"effect":[205],"decaying":[207],"quickly":[208],"M.":[211],"conclude,":[213],"consequence,":[215],"colored":[217],"asymptotically":[222],"good":[224],"working":[225],"choice":[234],"excitation":[237],"than":[238],"freedom":[246],"signal":[249],"design.":[250]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-14T08:36:36.166977","created_date":"2025-10-10T00:00:00"}