{"id":"https://openalex.org/W2089317779","doi":"https://doi.org/10.1109/tit.1979.1056103","title":"Digital adaptive filters: Conditions for convergence, rates of convergence, effects of noise and errors arising from the implementation","display_name":"Digital adaptive filters: Conditions for convergence, rates of convergence, effects of noise and errors arising from the implementation","publication_year":1979,"publication_date":"1979-11-01","ids":{"openalex":"https://openalex.org/W2089317779","doi":"https://doi.org/10.1109/tit.1979.1056103","mag":"2089317779"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1979.1056103","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1979.1056103","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/A5064597032","display_name":"A.J. Weiss","orcid":"https://orcid.org/0000-0001-7354-8219"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Weiss","raw_affiliation_strings":["Bell Laboratories, Inc., Murray Hill, NJ, USA","Courant Institute of Mathematical Sciences, New York University, Murray Hill, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Inc., Murray Hill, NJ, USA","institution_ids":[]},{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, Murray Hill, NY, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064391008","display_name":"Debasis Mitra","orcid":"https://orcid.org/0000-0002-4351-1252"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Mitra","raw_affiliation_strings":["Bell Laboratories, Inc., Murray Hill, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Inc., Murray Hill, NJ, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.0669,"has_fulltext":false,"cited_by_count":108,"citation_normalized_percentile":{"value":0.98850575,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"25","issue":"6","first_page":"637","last_page":"652"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13612","display_name":"Advanced Scientific and Engineering Studies","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T13612","display_name":"Advanced Scientific and Engineering Studies","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/T13018","display_name":"Seismology and Earthquake Studies","score":0.9677000045776367,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9559999704360962,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4345967471599579},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4279380440711975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3906824290752411}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4345967471599579},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4279380440711975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3906824290752411},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1979.1056103","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1979.1056103","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W970354589","https://openalex.org/W986645506","https://openalex.org/W1515682093","https://openalex.org/W1521581363","https://openalex.org/W1535810436","https://openalex.org/W1977651056","https://openalex.org/W1979690761","https://openalex.org/W1984819558","https://openalex.org/W1989695340","https://openalex.org/W2001553466","https://openalex.org/W2008965105","https://openalex.org/W2010473430","https://openalex.org/W2016261381","https://openalex.org/W2021648130","https://openalex.org/W2031530284","https://openalex.org/W2042665910","https://openalex.org/W2045978752","https://openalex.org/W2060962965","https://openalex.org/W2066686542","https://openalex.org/W2080621963","https://openalex.org/W2086066910","https://openalex.org/W2101415847","https://openalex.org/W2106329975","https://openalex.org/W2117481010","https://openalex.org/W2134883135","https://openalex.org/W2137928951","https://openalex.org/W2158796382","https://openalex.org/W2163634845","https://openalex.org/W3021259279","https://openalex.org/W4255373380","https://openalex.org/W6632223199","https://openalex.org/W6683558289","https://openalex.org/W6777023728"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2317200988","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829"],"abstract_inverted_index":{"A":[0],"variety":[1],"of":[2,11,102,111,145,159,216],"theoretical":[3],"results":[4,202],"are":[5,154,183,187],"derived":[6,155],"for":[7,141,156],"a":[8,23,62,127],"well-known":[9],"class":[10],"discrete-time":[12,24],"adaptive":[13],"filters.":[14],"First":[15],"the":[16,96,103,108,112,133,142,146,157,175,196,199],"following":[17],"idealized":[18,197],"identification":[19],"problem":[20],"is":[21,45,95,105,124,137,164,181,192],"considered:":[22],"system":[25],"has":[26],"vector":[27,57,114,177],"input":[28,210,221],"<tex":[29,35,42,58,67,82,92,115,167,171,178],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[30,36,43,59,68,83,93,116,168,172,179],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x(t)</tex>":[31,173],"and":[32,91,139,151,170,174,190],"scalar":[33],"output":[34],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">z(t)=":[37],"h":[38,119],"\\'":[39,88],"x(t)</tex>":[40],"where":[41,81,162],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">h</tex>":[44,180],"an":[46,55],"unknown":[47],"time-invariant":[48],"coefficient":[49,176],"vector.":[50],"The":[51,100],"filter":[52,104],"considered":[53],"adjusts":[54],"estimate":[56],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\hat{h}(t)</tex>":[60],"in":[61,166,195,211],"control":[63,97],"loop":[64,98],"according":[65],"to":[66,219],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\hat{h}(t":[69],"+":[70,75],"\\Delta":[71],"t)":[72,87],"=":[73,118],"\\hat{h}(t)":[74],"K[z(t)":[76],"-":[77,120,222],"\\hat{z}":[78],"(t)]x(t)</tex>":[79],",":[80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\hat{z}(":[84],"t)=":[85],"\\hat{h}(":[86],"x(":[89],"t)</tex>":[90],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">K</tex>":[94],"gain.":[99],"effectiveness":[101],"determined":[106],"by":[107],"convergence":[109,144],"properties":[110],"misalignment":[113],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r(t)":[117],"\\hat{h}(t)</tex>":[121],".":[122],"It":[123],"shown":[125,193],"that":[126,194],"certain":[128,214],"nondegeneracy":[129],"\"mixing\"":[130],"condition":[131],"on":[132],"Input":[134],"{":[135],"x(t)}":[136],"necessary":[138],"sufficient":[140],"exponential":[143],"misalignment.":[147],"Qualitatively":[148],"identical":[149],"upper":[150],"lower":[152],"bounds":[153],"rate":[158],"convergence.":[160],"Situations":[161],"noise":[163,217],"present":[165],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">z(t)</tex>":[169],"time-varying":[182],"analyzed.":[184],"Nonmixing":[185],"inputs":[186],"also":[188],"considered,":[189],"it":[191],"model":[198],"above":[200],"stability":[201],"apply":[203],"with":[204,213],"only":[205],"minor":[206],"modifications.":[207],"However,":[208],"nonmixing":[209],"conjunction":[212],"types":[215],"lead":[218],"bounded":[220],"unbounded":[223],"output,":[224],"i.e.,":[225],"instability.":[226]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
