{"id":"https://openalex.org/W2165591509","doi":"https://doi.org/10.1155/s1110865701000348","title":"Adaptive Filters with Error Nonlinearities: Mean-Square Analysis and Optimum Design","display_name":"Adaptive Filters with Error Nonlinearities: Mean-Square Analysis and Optimum Design","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2165591509","doi":"https://doi.org/10.1155/s1110865701000348","mag":"2165591509"},"language":"en","primary_location":{"id":"doi:10.1155/s1110865701000348","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s1110865701000348","pdf_url":null,"source":{"id":"https://openalex.org/S35920007","display_name":"EURASIP Journal on Advances in Signal Processing","issn_l":"1687-6172","issn":["1687-6172","1687-6180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Advances in Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1155/s1110865701000348","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066119580","display_name":"Tareq Y. Al-Naffouri","orcid":"https://orcid.org/0000-0001-6955-4720"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tareq Y. Al-Naffouri","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091103447","display_name":"Ali H. Sayed","orcid":"https://orcid.org/0000-0002-5125-5519"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ali H. Sayed","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066119580"],"corresponding_institution_ids":[],"apc_list":{"value":1140,"currency":"GBP","value_usd":1398},"apc_paid":{"value":1140,"currency":"GBP","value_usd":1398},"fwci":3.1726,"has_fulltext":false,"cited_by_count":121,"citation_normalized_percentile":{"value":0.91225806,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"2001","issue":"4","first_page":"192","last_page":"205"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10860","display_name":"Speech and Audio Processing","score":0.9922999739646912,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9897000193595886,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6889482736587524},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5596129894256592},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5478671193122864},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5222295522689819},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5180470943450928},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5094671845436096},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.5034775137901306},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.46711409091949463},{"id":"https://openalex.org/keywords/adaptive-filter","display_name":"Adaptive filter","score":0.45625054836273193},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.4524591565132141},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.45180997252464294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4511616826057434},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4318305552005768},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.41964587569236755},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3539764881134033},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2775909900665283},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.22745710611343384},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08993884921073914}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6889482736587524},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5596129894256592},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5478671193122864},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5222295522689819},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5180470943450928},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5094671845436096},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.5034775137901306},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.46711409091949463},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.45625054836273193},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.4524591565132141},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.45180997252464294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4511616826057434},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4318305552005768},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.41964587569236755},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3539764881134033},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2775909900665283},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.22745710611343384},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08993884921073914},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/s1110865701000348","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s1110865701000348","pdf_url":null,"source":{"id":"https://openalex.org/S35920007","display_name":"EURASIP Journal on Advances in Signal Processing","issn_l":"1687-6172","issn":["1687-6172","1687-6180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Advances in Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:62ac5377468248e5bbdfc531f77037aa","is_oa":true,"landing_page_url":"https://doaj.org/article/62ac5377468248e5bbdfc531f77037aa","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"EURASIP Journal on Advances in Signal Processing, Vol 2001, Iss 4, p 560906 (2001)","raw_type":"article"},{"id":"pmh:oai:infoscience.epfl.ch:233095","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/233095","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1155/s1110865701000348","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s1110865701000348","pdf_url":null,"source":{"id":"https://openalex.org/S35920007","display_name":"EURASIP Journal on Advances in Signal Processing","issn_l":"1687-6172","issn":["1687-6172","1687-6180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Advances in Signal Processing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W306463231","https://openalex.org/W1492221128","https://openalex.org/W1542146643","https://openalex.org/W1553032475","https://openalex.org/W1575706993","https://openalex.org/W1854272764","https://openalex.org/W1952987489","https://openalex.org/W1971289843","https://openalex.org/W2001905757","https://openalex.org/W2004534752","https://openalex.org/W2018774667","https://openalex.org/W2051339135","https://openalex.org/W2056931328","https://openalex.org/W2072148858","https://openalex.org/W2096093732","https://openalex.org/W2096915734","https://openalex.org/W2097488004","https://openalex.org/W2097715461","https://openalex.org/W2098225975","https://openalex.org/W2111411409","https://openalex.org/W2116059849","https://openalex.org/W2122742785","https://openalex.org/W2124278229","https://openalex.org/W2128115636","https://openalex.org/W2128495863","https://openalex.org/W2131865114","https://openalex.org/W2136143959","https://openalex.org/W2140595879","https://openalex.org/W2148652761","https://openalex.org/W2155031132","https://openalex.org/W2162725450","https://openalex.org/W2498643698","https://openalex.org/W2801179766","https://openalex.org/W3016843226"],"related_works":["https://openalex.org/W2102148524","https://openalex.org/W3102623159","https://openalex.org/W2314720829","https://openalex.org/W4385074335","https://openalex.org/W2366911843","https://openalex.org/W2626189183","https://openalex.org/W2350577681","https://openalex.org/W2322239237","https://openalex.org/W2360117988","https://openalex.org/W2778252020"],"abstract_inverted_index":{"This":[0],"paper":[1,20],"develops":[2],"a":[3,74],"unified":[4],"approach":[5],"to":[6,61,72,90,93],"the":[7,19,40,48,53,66,77,82,94],"analysis":[8,25,56],"and":[9,23,42],"design":[10],"of":[11,26,29,52,76,81],"adaptive":[12],"filters":[13,30],"with":[14],"error":[15],"nonlinearities.":[16],"In":[17],"particular,":[18],"performs":[21],"stability":[22],"steady-state":[24],"this":[27],"class":[28],"under":[31],"weaker":[32],"conditions":[33],"than":[34],"what":[35],"is":[36,101],"usually":[37],"encountered":[38],"in":[39],"literature,":[41],"without":[43],"imposing":[44],"any":[45],"restriction":[46],"on":[47,103],"color":[49],"or":[50],"statistics":[51],"input.":[54],"The":[55,97],"results":[57],"are":[58,88],"subsequently":[59],"used":[60],"derive":[62],"an":[63],"expression":[64],"for":[65],"optimum":[67,95],"nonlinearity,":[68],"which":[69],"turns":[70],"out":[71],"be":[73,91],"function":[75,80],"probability":[78],"density":[79],"estimation":[83],"error.":[84],"Some":[85],"common":[86],"nonlinearities":[87],"shown":[89],"approximations":[92],"nonlinearity.":[96],"framework":[98],"pursued":[99],"here":[100],"based":[102],"energy":[104],"conservation":[105],"arguments.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}