{"id":"https://openalex.org/W2143890950","doi":"https://doi.org/10.1109/tit.1968.1054131","title":"The uncorrelated output components of a nonlinearity","display_name":"The uncorrelated output components of a nonlinearity","publication_year":1968,"publication_date":"1968-03-01","ids":{"openalex":"https://openalex.org/W2143890950","doi":"https://doi.org/10.1109/tit.1968.1054131","mag":"2143890950"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1968.1054131","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1968.1054131","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5046866442","display_name":"Nelson M. Blachman","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"N. Blachman","raw_affiliation_strings":["Sylvania Electronics Systems, Inc., Mountain View, CA, USA","[Sylvania Electronics Systems, Inc., Mountain View, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Sylvania Electronics Systems, Inc., Mountain View, CA, USA","institution_ids":[]},{"raw_affiliation_string":"[Sylvania Electronics Systems, Inc., Mountain View, CA, USA]","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046866442"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6146,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.71212121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"14","issue":"2","first_page":"250","last_page":"255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9879000186920166,"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":0.9879000186920166,"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/T10320","display_name":"Neural Networks and Applications","score":0.9801999926567078,"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/T11236","display_name":"Control Systems and Identification","score":0.9746000170707703,"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/autocorrelation","display_name":"Autocorrelation","score":0.788960874080658},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7571976780891418},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5961413383483887},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5693455338478088},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.5674207806587219},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.5413172245025635},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.5279927253723145},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5278836488723755},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5169350504875183},{"id":"https://openalex.org/keywords/uncorrelated","display_name":"Uncorrelated","score":0.48498010635375977},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.46983879804611206},{"id":"https://openalex.org/keywords/autocorrelation-matrix","display_name":"Autocorrelation matrix","score":0.46001526713371277},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.4244965612888336},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4177485704421997},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34854423999786377},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2913932204246521},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20802003145217896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12420758605003357},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11939108371734619}],"concepts":[{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.788960874080658},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7571976780891418},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5961413383483887},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5693455338478088},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.5674207806587219},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.5413172245025635},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5279927253723145},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5278836488723755},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5169350504875183},{"id":"https://openalex.org/C169345407","wikidata":"https://www.wikidata.org/wiki/Q8216221","display_name":"Uncorrelated","level":2,"score":0.48498010635375977},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46983879804611206},{"id":"https://openalex.org/C4033963","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation matrix","level":3,"score":0.46001526713371277},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.4244965612888336},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4177485704421997},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34854423999786377},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2913932204246521},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20802003145217896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12420758605003357},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11939108371734619},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1968.1054131","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1968.1054131","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1975270170","https://openalex.org/W1991302453","https://openalex.org/W1995117140","https://openalex.org/W1995269534","https://openalex.org/W2002851938","https://openalex.org/W2010484705","https://openalex.org/W2022198558","https://openalex.org/W2081649012","https://openalex.org/W2114509411","https://openalex.org/W2121055926","https://openalex.org/W2133741398","https://openalex.org/W2160465108","https://openalex.org/W3136463145","https://openalex.org/W4205251719"],"related_works":["https://openalex.org/W2149192747","https://openalex.org/W2007192445","https://openalex.org/W2313872725","https://openalex.org/W2048784594","https://openalex.org/W2052532834","https://openalex.org/W2105045607","https://openalex.org/W2733003446","https://openalex.org/W2013878881","https://openalex.org/W2022021973","https://openalex.org/W2359476090"],"abstract_inverted_index":{"Using":[0],"his":[1],"characteristic-function":[2],"approach,":[3],"Rice":[4],"(1945)":[5],"obtained":[6],"a":[7,15,24,57,115],"double":[8,54,128],"series":[9],"for":[10,123],"the":[11,32,35,41,50,60,72,78,82,90,108,124],"autocorrelation":[12],"function":[13],"of":[14,34,43,52,59,77],"sinusoidal":[16,109],"signal":[17,80],"and":[18,69,81,96,110,118],"Gaussian":[19,111],"noise":[20,84],"after":[21],"passage":[22],"through":[23],"memoryless":[25],"nonlinearity.":[26],"It":[27],"is":[28,62,121],"shown":[29,63],"here":[30],"that":[31],"output":[33,61],"nonlinearity":[36],"can":[37,85,106],"be":[38,65,87],"expressed":[39,88],"as":[40,104],"sum":[42],"uncorrelated":[44],"terms":[45,51],"whose":[46],"auto-correlation":[47],"functions":[48,76],"are":[49],"Rice's":[53,127],"series.":[55,129],"Such":[56],"decomposition":[58],"to":[64],"generally":[66],"possible":[67],"if":[68,71],"only":[70],"bivariate":[73],"probability":[74],"density":[75],"input":[79,83],"both":[86],"in":[89,107,126],"diagonal":[91],"form":[92],"studied":[93],"by":[94],"Barrett":[95],"Lampard":[97],"(1955),":[98],"though":[99],"not":[100],"necessarily":[101],"involving":[102],"polynomials,":[103],"they":[105],"cases.":[112],"In":[113],"addition,":[114],"more":[116],"direct":[117],"meaningful":[119],"equation":[120],"found":[122],"coefficients":[125]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
