{"id":"https://openalex.org/W2139570824","doi":"https://doi.org/10.1109/tit.1984.1056849","title":"Lattice filter parameterization and modeling of nonstationary processes","display_name":"Lattice filter parameterization and modeling of nonstationary processes","publication_year":1984,"publication_date":"1984-01-01","ids":{"openalex":"https://openalex.org/W2139570824","doi":"https://doi.org/10.1109/tit.1984.1056849","mag":"2139570824"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1984.1056849","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1984.1056849","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/A5040128027","display_name":"H. Lev-Ari","orcid":"https://orcid.org/0000-0003-1937-5702"},"institutions":[{"id":"https://openalex.org/I4210141677","display_name":"Integrated Systems Solutions (United States)","ror":"https://ror.org/0422rme67","country_code":"US","type":"company","lineage":["https://openalex.org/I4210141677"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. Lev-Ari","raw_affiliation_strings":["Integrated Systems, Inc., Palo Alto, CA, USA","[Integrated Systems, Inc., Palo Alto, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Integrated Systems, Inc., Palo Alto, CA, USA","institution_ids":["https://openalex.org/I4210141677"]},{"raw_affiliation_string":"[Integrated Systems, Inc., Palo Alto, CA, USA]","institution_ids":["https://openalex.org/I4210141677"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014088470","display_name":"T. Kailath","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Kailath","raw_affiliation_strings":["Department of Electrical Engineering, University of Stanford, Stanford, CA, USA","[Department of Electrical Engineering, University of Stanford, Stanford, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"[Department of Electrical Engineering, University of Stanford, Stanford, CA, USA]","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.426,"has_fulltext":false,"cited_by_count":111,"citation_normalized_percentile":{"value":0.99273561,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"1","first_page":"2","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9916999936103821,"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"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9914000034332275,"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/mathematics","display_name":"Mathematics","score":0.7129523158073425},{"id":"https://openalex.org/keywords/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.6257628798484802},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6194890141487122},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.4863308072090149},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4862267076969147},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4790138602256775},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.4384768605232239},{"id":"https://openalex.org/keywords/lattice-phase-equaliser","display_name":"Lattice phase equaliser","score":0.42337071895599365},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38347217440605164},{"id":"https://openalex.org/keywords/adaptive-filter","display_name":"Adaptive filter","score":0.20416149497032166},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15766960382461548}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7129523158073425},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.6257628798484802},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6194890141487122},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.4863308072090149},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4862267076969147},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4790138602256775},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.4384768605232239},{"id":"https://openalex.org/C111104540","wikidata":"https://www.wikidata.org/wiki/Q1807061","display_name":"Lattice phase equaliser","level":3,"score":0.42337071895599365},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38347217440605164},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.20416149497032166},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15766960382461548},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","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/tit.1984.1056849","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1984.1056849","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":32,"referenced_works":["https://openalex.org/W40758387","https://openalex.org/W359317354","https://openalex.org/W1528659953","https://openalex.org/W1557675779","https://openalex.org/W1576783654","https://openalex.org/W1606124404","https://openalex.org/W1964919148","https://openalex.org/W1970369302","https://openalex.org/W1986280275","https://openalex.org/W1995432522","https://openalex.org/W2004823017","https://openalex.org/W2006164426","https://openalex.org/W2010961009","https://openalex.org/W2026305044","https://openalex.org/W2035288273","https://openalex.org/W2041165203","https://openalex.org/W2050622140","https://openalex.org/W2055547925","https://openalex.org/W2060594652","https://openalex.org/W2072079032","https://openalex.org/W2083862580","https://openalex.org/W2109820564","https://openalex.org/W2126832605","https://openalex.org/W2143822684","https://openalex.org/W2164323769","https://openalex.org/W2167364253","https://openalex.org/W3145946059","https://openalex.org/W4241280266","https://openalex.org/W4246360657","https://openalex.org/W4250038851","https://openalex.org/W4301807748","https://openalex.org/W6633324310"],"related_works":["https://openalex.org/W2153421756","https://openalex.org/W4239315977","https://openalex.org/W2077818434","https://openalex.org/W2054489697","https://openalex.org/W2361081803","https://openalex.org/W2614210101","https://openalex.org/W2036241269","https://openalex.org/W4250375811","https://openalex.org/W2175045955","https://openalex.org/W1646666949"],"abstract_inverted_index":{"A":[0,15,101],"general":[1],"theory":[2],"of":[3,18,23,39,48,58,90,94,104,144,154,161],"constant-parameter":[4,102],"modular":[5],"lattice":[6,113],"models":[7],"for":[8,46,65,98,132],"discrete-time":[9],"nonstationary":[10,66,163],"second-order":[11],"processes":[12,20],"is":[13,28,81,108],"presented.":[14],"complete":[16],"parametrization":[17,160],"such":[19],"in":[21,169],"terms":[22],"Schur":[24,50,166],"and":[25,43,61,68],"congruence":[26,84,134],"coefficients":[27,77,85,135,167],"derived":[29,109],"by":[30,110,150,178],"developing":[31],"a":[32,40,53,91,112,117,129,137,162],"natural":[33],"connection":[34],"between":[35],"the":[36,72,79,87,95,99,105,133,145,152,159],"displacement":[37],"structure":[38,115],"covariance":[41,59,80],"matrix":[42],"Schur's":[44],"test":[45],"positive-definiteness":[47],"matrices.":[49],"coeffieients":[51],"provide":[52,86],"simple":[54],"solution":[55],"to":[56,165,171],"problems":[57],"extension":[60],"rational":[62],"spectral":[63],"approximation":[64],"covariances,":[67],"they":[69],"coincide":[70],"with":[71,116,122],"well-known":[73],"reflection":[74],"(or":[75],"PARCOR)":[76],"when":[78],"stationary.":[82],"The":[83,141],"time-varying":[88],"gains":[89],"tapped-delay-line":[92,142],"realization":[93,103,146],"whitening":[96],"filter":[97,107,114],"process.":[100],"same":[106],"combining":[111],"tapped":[118],"delay":[119],"line,":[120],"both":[121],"time-invariant":[123],"gains.":[124],"This":[125],"configuration":[126],"also":[127,157],"provides":[128],"recursive":[130],"relation":[131],"(namely,":[136],"generalized":[138],"Levinson-Szego":[139],"recursion).":[140],"part":[143],"can":[147],"be":[148],"eliminated":[149],"introducing":[151],"concept":[153],"admissibility.":[155],"Admissibility":[156],"reduces":[158],"process":[164],"alone,":[168],"analogy":[170],"stationary":[172],"processes,":[173],"which":[174],"are":[175],"completely":[176],"characterized":[177],"their":[179],"PARCOR":[180],"coefficients.":[181]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}