{"id":"https://openalex.org/W2159071216","doi":"https://doi.org/10.1109/tsp.2011.2162954","title":"Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety","display_name":"Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety","publication_year":2011,"publication_date":"2011-08-03","ids":{"openalex":"https://openalex.org/W2159071216","doi":"https://doi.org/10.1109/tsp.2011.2162954","mag":"2159071216"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2162954","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2162954","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","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/A5060798483","display_name":"T\u00fclay Adal\u0131","orcid":"https://orcid.org/0000-0003-0594-2796"},"institutions":[{"id":"https://openalex.org/I79272384","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78","country_code":"US","type":"education","lineage":["https://openalex.org/I79272384"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Adali","raw_affiliation_strings":["Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD, USA","institution_ids":["https://openalex.org/I79272384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006601601","display_name":"Peter J. Schreier","orcid":"https://orcid.org/0000-0001-8481-7031"},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"P. J. Schreier","raw_affiliation_strings":["Signal and System Theory Group, Universit\u00e4t Paderborn, Paderborn, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Signal and System Theory Group, Universit\u00e4t Paderborn, Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080469112","display_name":"Louis L. Scharf","orcid":"https://orcid.org/0000-0003-1764-9335"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. L. Scharf","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA","institution_ids":["https://openalex.org/I92446798"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":22.4363,"has_fulltext":false,"cited_by_count":402,"citation_normalized_percentile":{"value":0.99701631,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"59","issue":"11","first_page":"5101","last_page":"5125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/appearance-of-impropriety","display_name":"Appearance of impropriety","score":0.8685426115989685},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.5938128232955933},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5367245674133301},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5199200510978699},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.5139048099517822},{"id":"https://openalex.org/keywords/statistical-signal-processing","display_name":"Statistical signal processing","score":0.5106099247932434},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5055062770843506},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.48380011320114136},{"id":"https://openalex.org/keywords/complex-normal-distribution","display_name":"Complex normal distribution","score":0.4544031322002411},{"id":"https://openalex.org/keywords/complex-conjugate","display_name":"Complex conjugate","score":0.4498816430568695},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.4463808834552765},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.44542941451072693},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4441298842430115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.418578565120697},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3554639220237732},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3362695574760437},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.19282686710357666},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14748799800872803},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.11716234683990479}],"concepts":[{"id":"https://openalex.org/C55507652","wikidata":"https://www.wikidata.org/wiki/Q4780990","display_name":"Appearance of impropriety","level":2,"score":0.8685426115989685},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.5938128232955933},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5367245674133301},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5199200510978699},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.5139048099517822},{"id":"https://openalex.org/C105125183","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Statistical signal processing","level":4,"score":0.5106099247932434},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5055062770843506},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.48380011320114136},{"id":"https://openalex.org/C201080289","wikidata":"https://www.wikidata.org/wiki/Q5156587","display_name":"Complex normal distribution","level":3,"score":0.4544031322002411},{"id":"https://openalex.org/C45542137","wikidata":"https://www.wikidata.org/wiki/Q381040","display_name":"Complex conjugate","level":2,"score":0.4498816430568695},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.4463808834552765},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.44542941451072693},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4441298842430115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.418578565120697},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3554639220237732},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3362695574760437},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.19282686710357666},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14748799800872803},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.11716234683990479},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2011.2162954","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2162954","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:mdsoar.org:11603/12728","is_oa":false,"landing_page_url":"http://hdl.handle.net/11603/12728","pdf_url":null,"source":{"id":"https://openalex.org/S4306402556","display_name":"Maryland Shared Open Access Repository (USMAI Consortium)","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":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/1","score":0.5400000214576721,"display_name":"No poverty"}],"awards":[{"id":"https://openalex.org/G5533259708","display_name":"Collaborative Research: SEI: Independent Component Analysis of Complex-Valued Brain Imaging Data","funder_award_id":"0612076","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7336460260","display_name":"Collaborative Research: Complex-Valued Signal Processing and its Application to Analysis of Brain Imaging Data","funder_award_id":"0635129","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8469529047","display_name":null,"funder_award_id":"FA 9550-10-1-0241","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320273","display_name":"University of Cambridge","ror":"https://ror.org/013meh722"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":155,"referenced_works":["https://openalex.org/W12260108","https://openalex.org/W53790464","https://openalex.org/W81722178","https://openalex.org/W87496662","https://openalex.org/W186621202","https://openalex.org/W639989723","https://openalex.org/W1002377575","https://openalex.org/W1491109205","https://openalex.org/W1491758811","https://openalex.org/W1535810436","https://openalex.org/W1548802052","https://openalex.org/W1586217171","https://openalex.org/W1755563775","https://openalex.org/W1868590549","https://openalex.org/W1877665914","https://openalex.org/W1972087067","https://openalex.org/W1974388905","https://openalex.org/W1977743341","https://openalex.org/W1978979650","https://openalex.org/W1983791336","https://openalex.org/W1999666226","https://openalex.org/W2002714615","https://openalex.org/W2003335470","https://openalex.org/W2010550144","https://openalex.org/W2010961394","https://openalex.org/W2017546712","https://openalex.org/W2022165146","https://openalex.org/W2023413246","https://openalex.org/W2028002800","https://openalex.org/W2030127857","https://openalex.org/W2032042468","https://openalex.org/W2033644905","https://openalex.org/W2036043111","https://openalex.org/W2037095848","https://openalex.org/W2054658115","https://openalex.org/W2065234731","https://openalex.org/W2067489830","https://openalex.org/W2069222481","https://openalex.org/W2076900674","https://openalex.org/W2078585350","https://openalex.org/W2082191514","https://openalex.org/W2082542187","https://openalex.org/W2083671377","https://openalex.org/W2088025772","https://openalex.org/W2088937325","https://openalex.org/W2092490046","https://openalex.org/W2095632977","https://openalex.org/W2096380790","https://openalex.org/W2096710051","https://openalex.org/W2098628688","https://openalex.org/W2098918476","https://openalex.org/W2099741732","https://openalex.org/W2103406330","https://openalex.org/W2104324668","https://openalex.org/W2105271339","https://openalex.org/W2105767219","https://openalex.org/W2106995321","https://openalex.org/W2108384452","https://openalex.org/W2108746992","https://openalex.org/W2109410952","https://openalex.org/W2109772910","https://openalex.org/W2112345337","https://openalex.org/W2112935129","https://openalex.org/W2113257416","https://openalex.org/W2114347718","https://openalex.org/W2114382976","https://openalex.org/W2114765937","https://openalex.org/W2115074110","https://openalex.org/W2115711088","https://openalex.org/W2115874509","https://openalex.org/W2117993860","https://openalex.org/W2120953602","https://openalex.org/W2123399269","https://openalex.org/W2123827510","https://openalex.org/W2124677862","https://openalex.org/W2124757684","https://openalex.org/W2127395378","https://openalex.org/W2127737934","https://openalex.org/W2127949350","https://openalex.org/W2128552251","https://openalex.org/W2128967371","https://openalex.org/W2129152588","https://openalex.org/W2130288073","https://openalex.org/W2133777702","https://openalex.org/W2133885245","https://openalex.org/W2134238797","https://openalex.org/W2136284422","https://openalex.org/W2136424517","https://openalex.org/W2136594511","https://openalex.org/W2137044065","https://openalex.org/W2137977844","https://openalex.org/W2139665679","https://openalex.org/W2139996618","https://openalex.org/W2140638323","https://openalex.org/W2141171905","https://openalex.org/W2141224535","https://openalex.org/W2142635246","https://openalex.org/W2143110984","https://openalex.org/W2143410296","https://openalex.org/W2143646747","https://openalex.org/W2145624369","https://openalex.org/W2149470797","https://openalex.org/W2149781749","https://openalex.org/W2152819669","https://openalex.org/W2153999007","https://openalex.org/W2155260992","https://openalex.org/W2156105064","https://openalex.org/W2156142408","https://openalex.org/W2156782020","https://openalex.org/W2159566873","https://openalex.org/W2161735865","https://openalex.org/W2162747898","https://openalex.org/W2164997031","https://openalex.org/W2165415702","https://openalex.org/W2166288622","https://openalex.org/W2167705656","https://openalex.org/W2168175751","https://openalex.org/W2168930471","https://openalex.org/W2169571074","https://openalex.org/W2169920041","https://openalex.org/W2170922689","https://openalex.org/W2171674545","https://openalex.org/W2182579923","https://openalex.org/W2261609051","https://openalex.org/W2280399218","https://openalex.org/W2294288691","https://openalex.org/W2476841360","https://openalex.org/W2498575841","https://openalex.org/W2544829973","https://openalex.org/W2546768029","https://openalex.org/W2595378026","https://openalex.org/W2610857016","https://openalex.org/W2729347441","https://openalex.org/W3010812135","https://openalex.org/W3095095911","https://openalex.org/W3100792434","https://openalex.org/W3103391113","https://openalex.org/W3140025309","https://openalex.org/W3146835983","https://openalex.org/W4205778870","https://openalex.org/W4211251910","https://openalex.org/W4212793308","https://openalex.org/W4230891582","https://openalex.org/W4240292324","https://openalex.org/W4242259102","https://openalex.org/W4247480362","https://openalex.org/W4285719527","https://openalex.org/W4297913868","https://openalex.org/W4300472792","https://openalex.org/W6632223199","https://openalex.org/W6678415016","https://openalex.org/W6679066064","https://openalex.org/W6685931672","https://openalex.org/W6693036072","https://openalex.org/W6695396417"],"related_works":["https://openalex.org/W317794076","https://openalex.org/W4255290330","https://openalex.org/W4317878703","https://openalex.org/W1986825993","https://openalex.org/W3101410667","https://openalex.org/W4246821150","https://openalex.org/W1503114023","https://openalex.org/W2086043755","https://openalex.org/W2026884494","https://openalex.org/W2159071216"],"abstract_inverted_index":{"Complex-valued":[0],"signals":[1,29,82],"occur":[2],"in":[3,60,113,172],"many":[4,75],"areas":[5],"of":[6,13,87,101,118,127,135,175,182],"science":[7],"and":[8,10,45,79,94,131,162,186],"engineering":[9],"are":[11,30,67,74,83,109,155],"thus":[12],"fundamental":[14],"interest.":[15],"In":[16,144],"the":[17,61,88,98,114,123,133,150,173,180],"past,":[18],"it":[19],"has":[20,51],"often":[21],"been":[22],"assumed,":[23],"usually":[24],"implicitly,":[25],"that":[26,55],"complex":[27,36,43,48,62,142],"random":[28,37,49,81,129],"proper":[31,35,78],"or":[32],"circular.":[33],"A":[34],"variable":[38,50],"is":[39,56],"uncorrelated":[40],"with":[41,139],"its":[42],"conjugate,":[44],"a":[46,52],"circular":[47,80],"probability":[53],"distribution":[54],"invariant":[57],"under":[58],"rotation":[59],"plane.":[63],"While":[64],"these":[65],"assumptions":[66],"convenient":[68],"because":[69],"they":[70],"simplify":[71],"computations,":[72],"there":[73],"cases":[76],"where":[77],"very":[84],"poor":[85],"models":[86],"underlying":[89],"physics.":[90],"When":[91],"taking":[92],"impropriety":[93],"noncircularity":[95],"into":[96],"account,":[97],"right":[99],"type":[100],"processing":[102,117],"can":[103],"provide":[104],"significant":[105],"performance":[106],"gains.":[107],"There":[108],"two":[110],"key":[111],"ingredients":[112],"statistical":[115,125,160],"signal":[116,177],"complex-valued":[119,128,176],"data:":[120],"1)":[121],"utilizing":[122],"complete":[124],"characterization":[126],"signals;":[130],"2)":[132],"optimization":[134],"real-valued":[136],"cost":[137],"functions":[138],"respect":[140],"to":[141],"parameters.":[143],"this":[145],"overview":[146],"article,":[147],"we":[148],"review":[149],"necessary":[151],"tools,":[152],"among":[153],"which":[154],"widely":[156],"linear":[157],"transformations,":[158],"augmented":[159],"descriptions,":[161],"Wirtinger":[163],"calculus.":[164],"We":[165],"also":[166],"present":[167],"some":[168],"selected":[169],"recent":[170],"developments":[171],"field":[174],"processing,":[178],"addressing":[179],"topics":[181],"model":[183],"selection,":[184],"filtering,":[185],"source":[187],"separation.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":23},{"year":2022,"cited_by_count":24},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":23},{"year":2019,"cited_by_count":37},{"year":2018,"cited_by_count":57},{"year":2017,"cited_by_count":31},{"year":2016,"cited_by_count":36},{"year":2015,"cited_by_count":35},{"year":2014,"cited_by_count":31},{"year":2013,"cited_by_count":27},{"year":2012,"cited_by_count":15}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}