{"id":"https://openalex.org/W2121484311","doi":"https://doi.org/10.1109/icassp.2003.1201782","title":"The Karhunen-Loeve expansion of improper complex random signals with applications in detection","display_name":"The Karhunen-Loeve expansion of improper complex random signals with applications in detection","publication_year":2004,"publication_date":"2004-03-22","ids":{"openalex":"https://openalex.org/W2121484311","doi":"https://doi.org/10.1109/icassp.2003.1201782","mag":"2121484311"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2003.1201782","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2003.1201782","pdf_url":null,"source":{"id":"https://openalex.org/S4363608982","display_name":"2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).","raw_type":"proceedings-article"},"type":"conference-paper","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/A5006601601","display_name":"Peter J. Schreier","orcid":"https://orcid.org/0000-0001-8481-7031"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P.J. Schreier","raw_affiliation_strings":["Electrical & Computer Engineering, Univ. of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical & Computer Engineering, Univ. of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"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":["Electrical & Computer Eng. and Statistics, Colorado State University, CO"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical & Computer Eng. and Statistics, Colorado State University, CO","institution_ids":["https://openalex.org/I92446798"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"1","issue":null,"first_page":"VI","last_page":"717"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9990000128746033,"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":0.9990000128746033,"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/karhunen\u2013lo\u00e8ve-theorem","display_name":"Karhunen\u2013Lo\u00e8ve theorem","score":0.9712991118431091},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6285169124603271},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6048222780227661},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5358089208602905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5296727418899536},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.5257956385612488},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.4955860376358032},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4837956130504608},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4533001482486725},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.44125962257385254},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4369277358055115},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.42590367794036865},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36555466055870056},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3319215774536133},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3282730281352997},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24231192469596863},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1924145519733429},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09729522466659546},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08457398414611816}],"concepts":[{"id":"https://openalex.org/C109308471","wikidata":"https://www.wikidata.org/wiki/Q2046647","display_name":"Karhunen\u2013Lo\u00e8ve theorem","level":2,"score":0.9712991118431091},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6285169124603271},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6048222780227661},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5358089208602905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5296727418899536},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.5257956385612488},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.4955860376358032},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4837956130504608},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4533001482486725},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.44125962257385254},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4369277358055115},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.42590367794036865},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36555466055870056},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3319215774536133},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3282730281352997},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24231192469596863},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1924145519733429},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09729522466659546},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08457398414611816},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.2003.1201782","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2003.1201782","pdf_url":null,"source":{"id":"https://openalex.org/S4363608982","display_name":"2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2067489830","https://openalex.org/W2123827510","https://openalex.org/W2152362799","https://openalex.org/W2333780457","https://openalex.org/W6702770466"],"related_works":["https://openalex.org/W417204388","https://openalex.org/W187821709","https://openalex.org/W1963647550","https://openalex.org/W2730780850","https://openalex.org/W1974392290","https://openalex.org/W3103566292","https://openalex.org/W2074565401","https://openalex.org/W1607924090","https://openalex.org/W2609263042","https://openalex.org/W2118378416"],"abstract_inverted_index":{"Non-stationary":[0],"complex":[1,65],"random":[2,66],"signals":[3,67],"are":[4],"in":[5,23,68],"general":[6],"improper":[7,36,49,64],"(not":[8],"circularly":[9],"symmetric),":[10],"which":[11,84],"means":[12],"that":[13,90],"their":[14],"complementary":[15,86],"covariance":[16],"is":[17,27],"non-zero.":[18],"Since":[19],"the":[20,35,54,59,74,79],"Karhunen-Loeve":[21,55],"expansion":[22,56],"its":[24],"known":[25],"form":[26],"only":[28],"valid":[29],"for":[30],"proper":[31],"processes,":[32],"we":[33,77],"derive":[34],"version":[37],"of":[38,45,61,81,105],"this":[39],"expansion.":[40],"It":[41],"produces":[42],"two":[43],"sets":[44],"eigenvalues":[46],"and":[47],"an":[48],"internal":[50],"description.":[51],"We":[52],"use":[53],"to":[57],"solve":[58],"problem":[60],"detecting":[62],"non-stationary":[63],"additive":[69],"white":[70],"Gaussian":[71],"noise.":[72],"Using":[73],"deflection":[75],"criterion":[76],"compare":[78],"performance":[80,96],"conventional":[82],"processing,":[83],"ignores":[85],"covariances,":[87],"with":[88],"processing":[89],"takes":[91],"these":[92],"into":[93],"account.":[94],"The":[95],"gain":[97],"can":[98],"be":[99],"as":[100,102],"great":[101],"a":[103],"factor":[104],"2.":[106]},"counts_by_year":[{"year":2020,"cited_by_count":3}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
